<Text-field style="Heading 1" layout="Heading 1">Introdu\303\247\303\243o</Text-field>

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Cap\303\255tulo 12

Regra da Cadeia para Derivadas

Uma omiss\303\243o da lista de regras de diferencia\303\247\303\243o \303\251 uma regra para derivar a composi\303\247\303\243o de fun\303\247\303\265es. A Regra da Cadeia preenche este vazio. Embora a Regra da Cadeia seja bastante simples de se enunciar, \303\251 importante que se torne competente em suas aplica\303\247\303\265es. Os Exemplos come\303\247am com uma revisita\303\247\303\243o do Exemplo 11.3 do Cap\303\255tulo 11 e ent\303\243o se movem para situa\303\247\303\265es mais complicadas.

O Tutor M\303\251todos de Diferencia\303\247\303\243o pode ser particularmente \303\272til enquanto voc\303\252 desenvolve sua per\303\255cia em usar a Regra da Cadeia. Mas lembre-se de que \303\251 tamb\303\251m necess\303\241rio aplicar a Regra da Cadeia a m\303\243o.

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">\303\215ndice de Termos</Text-field>

Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio do Maple; para mais informa\303\247\303\265es v\303\241 em Dicion\303\241rio Matem\303\241tico.

regra da cadeia

composi\303\247\303\243o

constante

cont\303\255nuo

grau

denominador

derivada

quociente das diferen\303\247as

diferen\303\247a

diferenci\303\241vel

diferenciada

diferencia\303\247\303\243o

avaliada

par

expoente

fator

fun\303\247\303\243o

limite

minimizar

numerador

polin\303\264mio

expoente

regra do produto

produto

prova

regra do quociente

quociente

fun\303\247\303\243o racional

rec\303\255proco

substitui\303\247\303\243o

valor

zero

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Inicializa\303\247\303\243o</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnRitGOkY9

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Composi\303\247\303\243o de Fun\303\247\303\265es </Text-field>

A fun\303\247\303\243o:

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

\303\251 a composi\303\247\303\243o das fun\303\247\303\265es 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 e 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 de modo que 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. Por isso, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJGRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== \303\251 chamada uma fun\303\247\303\243o composta .

O n\303\272mero LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJGRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1JI21uR0YkNiRRIjJGJ0Y+Rj5GPkY+RitGPg== \303\251 calculado ao substituir LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUY1LUkjbW5HRiQ2JFEiMkYnRjlGOQ== em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GOVEnbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEnJnBsdXM7RidGPy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSi8lKXN0cmV0Y2h5R0ZKLyUqc3ltbWV0cmljR0ZKLyUobGFyZ2VvcEdGSi8lLm1vdmFibGVsaW1pdHNHRkovJSdhY2NlbnRHRkovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZZLUY8NiRRIjFGJ0Y/Rj8= resultando 5; depois, elevando 5 ao cubo, resultando 125. A primeira fun\303\247\303\243o que deve ser avaliada ser\303\241 chamada fun\303\247\303\243o "interna", enquanto que a segunda fun\303\247\303\243o, aplicada logo depois dessa, ser\303\241 chamada fun\303\247\303\243o "externa". Embora se possa pensar em 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, ela mesma, como uma fun\303\247\303\243o composta, no contexto de deriva\303\247\303\243o isso n\303\243o ser\303\241 usualmente necess\303\241rio. O que \303\251 crucial para a deriva\303\247\303\243o \303\251 o reconhecimento correto das fun\303\247\303\265es internas e externas.

Usando nota\303\247\303\243o puramente funcional, a composi\303\247\303\243o das fun\303\247\303\265es LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= seria escrita 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. Usando esta nota\303\247\303\243o, o valor da fun\303\247\303\243o composta LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 expressa pela nota\303\247\303\243o 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. A nota\303\247\303\243o 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 em geral prova ser mais simples de usar. (A nota\303\247\303\243o funcional LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKSZjb21wZm47RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkwtRiw2JVEiZ0YnRi9GMkY5 parece muito mais a palavra "fog" e freq\303\274entemente \303\251 o que acontece.)

Exemplos adicionais de fun\303\247\303\265es compostas aparecem na Tabela 12.1.

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYkLUYjNiZGKy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRisvRjtRJ25vcm1hbEYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJ0YrRj0=

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21uR0YkNiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GLDYlUSJ4RicvRjZRJXRydWVGJy9GOVEnaXRhbGljRidGOA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GOVEnbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGPw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSRzaW5GJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RidGNy8lJmZlbmNlR0Y2LyUqc2VwYXJhdG9yR0Y2LyUpc3RyZXRjaHlHRjYvJSpzeW1tZXRyaWNHRjYvJShsYXJnZW9wR0Y2LyUubW92YWJsZWxpbWl0c0dGNi8lJ2FjY2VudEdGNi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RicvRjVRJXRydWVGJy9GOFEnaXRhbGljRidGN0Y3RjdGK0Y3

Tabela 12.1

Fun\303\247\303\265es Compostas 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 e suas partes componentes

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Enunciado da Regra da Cadeia</Text-field>

Deriva\303\247\303\243o de uma fun\303\247\303\243o composta geralmente requer a regra da cadeiaLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEiLkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8= De todas as regras de deriva\303\247\303\243o, a regra da cadeia \303\251 a mais importante, mais por raz\303\265es te\303\263ricas do que por necessidade imediata de avaliar derivadas de fun\303\247\303\265es espec\303\255ficas.

A Regra da Cadeia

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

Usando os termos fun\303\247\303\243o externa e fun\303\247\303\243o interna, uma interpreta\303\247\303\243o verbal da regra da cadeia seria

A derivada da fun\303\247\303\243o externa, avaliada na (em rela\303\247\303\243o a) fun\303\247\303\243o interna, vezes a derivada da fun\303\247\303\243o interna.

Uma interpreta\303\247\303\243o mais gr\303\241fica poderia ser dada se a fun\303\247\303\243o externa fosse pensada como uma "embalagem" e a fun\303\247\303\243o interna como o "material" embalado. Ent\303\243o, deriva\303\247\303\243o pela regra da cadeia fica:

A derivada da embalagem avaliada no "material embalado" vezes a derivada do material embalado

A frase mnem\303\264nica "a derivada do material embalado" \303\251 provavelmente a mais importante que se possa anexar ao estudo da regra da cadeia.

Teorema 12.1 \303\251 um enunciado formal da regra da cadeia.

Teorema 12.1: A Regra da Cadeia

Se f e g s\303\243o fun\303\247\303\265es diferenci\303\241veis tais que ambas 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 e 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 existam, ent\303\243o 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, a composi\303\247\303\243o de f com g, \303\251 diferenci\303\241vel em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e a derivada de F em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251

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

Existe um n\303\272mero consider\303\241vel de modos de interpretar e entender a Regra da Cadeia. Uma das mais \303\272teis \303\251 pensar a composi\303\247\303\243o como uma engrenagem. Por exemplo, se uma cadeiaest\303\241 sendo puxada atrav\303\251s de uma engrenagem de 53 dentes e se a engrenagem est\303\241 sendo girada a uma raz\303\243o de 100 revolu\303\247\303\265es por minuto, ent\303\243o a cadeia passa atrav\303\251s da engrenagem a uma raz\303\243o de (53 elos/revolu\303\247\303\243o)(100 revolu\303\247\303\265es/min) = 5300 elos/min. Note como a raz\303\243o composta \303\251 o produto de raz\303\265es individuais.

Uma outra maneira de olhar a Regra da Cadeia \303\251 escrever 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 e 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 de modo que 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 fica:

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

Esta perspectiva \303\251 muito \303\272til e pode ajudar a lembrar da f\303\263rmula da Regra da Cadeia. \303\211 preciso estar ciente de que, embora seja tentador justificar esta f\303\263rmula pelo cancelamento de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn do numerador e denominador, a real "prova" deste resultado deve ser estabelecida em termos de quocientes das diferen\303\247as (onde realmente temos uma fra\303\247\303\243o!). Aqui est\303\241 um esbo\303\247o dessa prova (com passos adicionais no in\303\255cio e no final para enfatizar a conex\303\243o da primeira forma da Regra da Cadeia):

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGL0YyRjlGOS1GLDYjUSFGJ0Y5

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiUtRiw2JVEoJkRlbHRhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiw2JVEidUYnL0Y4USV0cnVlRicvRjtRJ2l0YWxpY0YnRjotRiM2JUY0LUYsNiVRInhGJ0ZARkJGOi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGTi8lKWJldmVsbGVkR0Y5RitGOg==

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

Note que a passagem do terceiro para o quarto passo depende da implica\303\247\303\243o 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

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Deriva\303\247\303\243o da Regra da Cadeia </Text-field>

Os requerimentos exatos para f e g que fazem LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= diferenci\303\241vel ser\303\243o discutidos mais tarde.

Para determinar a derivada de F em termos de f, g, e suas derivadas, come\303\247a com a defini\303\247\303\243o da derivada:

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

Ly1JI0YnRzYiNiNJInhHRiUtSSZMaW1pdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYsJi1JImZHRiU2Iy1JImdHRiU2IywmRiciIiJJImhHRiVGN0Y3LUYxNiMtRjRGJiEiIkY3RjhGPC9GOCIiIQ==

Assumindo que g \303\251 diferenci\303\241vel em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, ent\303\243o g deve ser cont\303\255nua em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e, assim, para valores pequenos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, 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 pode ser aproximado por 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. Fazendo esta substitui\303\247\303\243o no quociente das diferen\303\247as pela defini\303\247\303\243o de 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 resulta em:

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

Ly1JI0YnRzYiNiNJInhHRiUtSSZMaW1pdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYsJi1JImZHRiU2IywmLUkiZ0dGJUYmIiIiKiYtSSNnJ0dGJUYmRjZJImhHRiVGNkY2RjYtRjE2I0Y0ISIiRjZGOkY9L0Y6IiIh

Este limite pode ser levado a uma forma que seja reconhec\303\255vel como uma derivada se fizermos:

L0kickc2IiomLUkjZydHRiQ2I0kieEdGJCIiIkkiaEdGJEYq

Com esta substitui\303\247\303\243o podemos escrever:

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

Ly1JI0YnRzYiNiNJInhHRiUtSSZMaW1pdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKigsJi1JImZHRiU2IywmLUkiZ0dGJUYmIiIiSSJyR0YlRjZGNi1GMTYjRjQhIiJGNkY3RjotSSNnJ0dGJUYmRjYvSSJoR0YlIiIh

Isto parece promissor. Como 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 \303\251 uma constante com respeito ao limite em h, e \303\251 finito, pode ser fatorado para fora do limite. Mais ainda: o limite quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= se aproxima de 0 pode ser equivalentemente declarado como um limite quando r se aproxima de 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 por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, obtendo:

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

Ly1JI0YnRzYiNiNJInhHRiUtSSZMaW1pdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKigsJi1JImZHRiU2IywmLUkiZ0dGJUYmIiIiSSJyR0YlRjZGNi1GMTYjRjQhIiJGNkY3RjotSSNnJ0dGJUYmRjYvRjciIiE=

ent\303\243o retira o fator 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, obtendo:

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

Ly1JI0YnRzYiNiNJInhHRiUqJi1JI2cnR0YlRiYiIiItSSZMaW1pdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYsJi1JImZHRiU2IywmLUkiZ0dGJUYmRitJInJHRiVGK0YrLUY1NiNGOCEiIkYrRjpGPS9GOiIiIUYr

O limite que resta agora pode ser identificado como a derivada de f, avaliada em 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. A maioria dos textos escreveria esta derivada como 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. Entretanto, a representa\303\247\303\243o t\303\255pica da regra da cadeia \303\251:

Se o Maple for solicitado para avaliar o limite restante, ele escrever\303\241 o resultado como:

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

Ly1JI0YnRzYiNiNJInhHRiUqJi1JI2cnR0YlRiYiIiItLUkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSJmR0YlNiMtSSJnR0YlRiZGKw==

onde a nota\303\247\303\243o 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 representa LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkZn4nRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw==, e a avalia\303\247\303\243o desta derivada no argumento 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 \303\251 representada por: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. Se a nota\303\247\303\243o-D do Maple \303\251 convertida para a nota\303\247\303\243o mais familiar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYsNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JVEjZHhGJ0Y1RjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkMvJSliZXZlbGxlZEdRJmZhbHNlRidGKy9GOVEnbm9ybWFsRic= , apareceria como:

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

Ly1JI0YnRzYiNiNJInhHRiUqJi1JI2cnR0YlRiYiIiItSSVldmFsRyUqcHJvdGVjdGVkRzYkLUklZGlmZkdGLjYkLUkiZkdGJTYjSSN0MUdGJUY2PCMvRjYtSSJnR0YlRiZGKw==

A simplifica\303\247\303\243o que podemos extrair do Maple \303\251:

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

Ly1JI0YnRzYiNiNJInhHRiUqJi1JI2cnR0YlRiYiIiItSSVldmFsRyUqcHJvdGVjdGVkRzYkLUklZGlmZkdGLjYkLUkiZkdGJTYjSSR0YXVHRiVGNjwjL0Y2LUkiZ0dGJUYmRis=

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplos</Text-field>

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 12.1: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> </Text-field>

A fun\303\247\303\243o

pode ser reconhecida como a composi\303\247\303\243o 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 se 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 e 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.

Pela Regra da Cadeia, a derivada LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSNGJ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUYjNiYtRjs2LVEiKEYnRj4vRkFGNkZDL0ZGRjZGR0ZJRktGTS9GUFEsMC4xNjY2NjY3ZW1GJy9GU0Zmbi1GIzYkLUYsNiVRInhGJ0Y0RjdGPi1GOzYtUSIpRidGPkZZRkNGWkZHRklGS0ZNRmVuL0ZTUSwwLjExMTExMTFlbUYnRj5GK0Y+RitGPg== \303\251 dada por:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0ZGLUYsNi1RIidGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUkobWZlbmNlZEdGJDYkLUYjNiYtRko2I1EhRictRiM2Ji1GSjYlUSJnRidGTUZQLUYsNi1RMCZBcHBseUZ1bmN0aW9uO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtRlY2JC1GIzYkLUZKNiVRInhGJ0ZNRlBGL0YvRi9GWkYvRi9GaW5GUkZfb0ZaRi8=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUkjbW5HRiQ2JFEiMkYnRi9GRi1GIzYmLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUkobWZlbmNlZEdGJDYkLUYjNiQtRlA2JVEieEYnRlNGVkYvRi9GL0ZPLUYsNi1RIidGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERmVuLUZQNiNRIUYnRi8=

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

Este resultado concorda com os resultados encontrados no Exemplo 11.3 do cap\303\255tulo Regras de Deriva\303\247\303\243o. Maple tamb\303\251m confirma este resultado via:

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCokKSwoKiQpSSJ4R0YoIiIlIiIiRjEqJiIiJEYxKUYvIiIjRjFGMUYxRjFGNUYxRi8sJCoqRjBGMUYsRjFGL0YxLCYqJkY1RjFGNEYxRjFGM0YxRjFGMQ==

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 12.2: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> </Text-field>

O poder e utilidade da Regra da Cadeia n\303\243o est\303\243o particularmente aparentes no Exemplo 12.1. Se o expoente for trocado por um inteiro maior, digamos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJuRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEjMjBGJ0Y+Rj5GK0Y+, ent\303\243o o problema se torna excessivamente complicado pela expans\303\243o ou Regra do Produto. A computa\303\247\303\243o desta derivada usando a Regra da Cadeia \303\251 essencialmente a mesma que foi usada no Exemplo 12.1.

Seja

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 = 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

onde 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 e 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.

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

Exatamente o mesmo resultado \303\251 obtido no Maple via:

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

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCokKSwoKiQpSSJ4R0YoIiIlIiIiRjEqJiIiJEYxKUYvIiIjRjFGMUYxRjEiIz9GMUYvLCQqKEY2RjEpRiwiIz5GMSwmKiZGMEYxKUYvRjNGMUYxKiYiIidGMUYvRjFGMUYxRjE=

De forma mais geral, para qualquer inteiro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, a derivada pela regra da cadeia seria:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSNkeEYnRjdGOkY9LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZJLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGPQ== 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.

No Maple, isto aparece como:

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

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCksKCokKUkieEdGKCIiJSIiIkYwKiYiIiRGMClGLiIiI0YwRjBGMEYwSSJuR0YoRi4sJCosRjRGMClGKywmRjVGMEYwISIiRjBGNUYwRi5GMCwmKiZGNEYwRjNGMEYwRjJGMEYwRjA=

onde 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, o s\303\255mbolo de uma derivada parcial, \303\251 usada no lugar do esperado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSNkeEYnRjdGOkY9LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZJLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGPQ==. Isto acontece porque o Maple n\303\243o pode expressar que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= deve ser tratado como uma constante.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 12.3: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> e Outras Derivadas de Ordens Superiores</Text-field>

A segunda derivada de uma fun\303\247\303\243o \303\251 a derivada da derivada da fun\303\247\303\243o, e a nota\303\247\303\243o \303\251 escrita como

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

O primeiro passo para computar a segunda derivada pela regra da cadeia \303\251 computar a primeira derivada. Isto foi feito no Exemplo 12.2. Para a fun\303\247\303\243o:

a primeira derivada \303\251:

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

Para encontrar a segunda derivada, as regras do produto e da cadeia s\303\243o usadas, resultando em:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSInRidGOUY7Rj5GQEZCRkRGRkZIRkpGTUZPLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEieEYnRi9GMkY5RjktRiw2I1EhRidGOQ==

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGL0YyRjlGOS1GLDYjUSFGJ0Y5

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERi8=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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8=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

A segunda derivada, computada diretamente no Maple, da fun\303\247\303\243o composta \303\251:

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

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JSokKSwoKiQpSSJ4R0YoIiIlIiIiRjEqJiIiJEYxKUYvIiIjRjFGMUYxRjEiIz9GMUYvRi8sJCooIiNTRjEsKkYzRjEqJiIkZCRGMUY0RjFGMSomIiR4JUYxRi5GMUYxKiYiJGUiRjEpRi8iIidGMUYxRjEpRiwiIz1GMUYx

Note que a terceira, quarta, quinta e qualquer derivada de ordem mais alta pode ser computada de modo similar, mas as computa\303\247\303\265es se tornar\303\243o cada vez mais complexas, como podem ser vistas nos seguintes c\303\241lculos do Maple.

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

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCokKSwoKiQpSSJ4R0YoIiIlIiIiRjEqJiIiJEYxKUYvIiIjRjFGMUYxRjEiIz9GMTclRi9GL0YvLCQqKiIkUyNGMUYvRjEsLCIkdCJGMSomIiVQckYxRjRGMUYxKiYiJixUIkYxRi5GMUYxKiYiJWckKkYxKUYvIiInRjFGMSomIiVhP0YxKUYvIiIpRjFGMUYxKUYsIiM8RjFGMQ==

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCokKSwoKiQpSSJ4R0YoIiIlIiIiRjEqJiIiJEYxKUYvIiIjRjFGMUYxRjEiIz9GMTcmRi9GL0YvRi8sJCooIiRTI0YxLDAiJHQiRjEqJiImdyZSRjFGNEYxRjEqJiInXFkoKUYxRi5GMUYxKiYiKGs/QSNGMSlGLyIiJ0YxRjEqJiIoUiIqPiNGMSlGLyIiKUYxRjEqJiInbXAnKkYxKUYvIiM1RjFGMSomIidlImUiRjEpRi8iIzdGMUYxRjEpRiwiIztGMUYx

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCokKSwoKiQpSSJ4R0YoIiIlIiIiRjEqJiIiJEYxKUYvIiIjRjFGMUYxRjEiIz9GMTcnRi9GL0YvRi9GLywkKioiJlMjPUYxRi9GMSwyIiVnN0YxKiYiJiZIKipGMUY0RjFGMSomIig8RlgiRjFGLkYxRjEqJiIobHJNJUYxKUYvIiInRjFGMSomIigmPlljRjEpRi8iIilGMUYxKiYiKCZcNlBGMSlGLyIjNUYxRjEqJiIoOmlAIkYxKUYvIiM3RjFGMSomIidlImUiRjEpRi8iIzlGMUYxRjEpRiwiIzpGMUYx

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCokKSwoKiQpSSJ4R0YoIiIlIiIiRjEqJiIiJEYxKUYvIiIjRjFGMUYxRjEiIz9GMTcoRi9GL0YvRi9GL0YvLCQqKCInK09GRjEsNiomIicheiF6RjEpRi8iIz1GMUYxKiYiKE5CTShGMSlGLyIjO0YxRjEqJiIpXWA9R0YxKUYvIiM5RjFGMSomIik0M1lkRjEpRi8iIzdGMUYxKiYiKUAlemgnRjEpRi8iIzVGMUYxKiYiKVg9Jj0lRjEpRi8iIilGMUYxKiYiKU5aaDdGMSlGLyIiJ0YxRjEqJiIoNVo5IkYxRi5GMUYxKiYiJnJ3I0YxRjRGMUYxIiMlKUYxRjEpRixGR0YxRjE=

Mais adiante, note que a deriva\303\247\303\243o reduz o grau de um polin\303\264mio de 1. Portanto, como 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\303\251 um polin\303\264mio de grau 80, a 80-\303\251sima derivada de F, 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, deve ser LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNiYtSSNtbkdGJDYkUSM4MEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RKCZtaW51cztGJ0Y3LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk9GM0Y3LUY7Ni1RIj1GJ0Y3Rj5GQUZDRkVGR0ZJRksvRk5RLDAuMjc3Nzc3OGVtRicvRlFGVi1GNDYkUSIwRidGN0Y3RitGNw==, isto \303\251, ser uma constante, como verificado no Maple por:

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

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2XXAqJCksKCokKUkieEdGKCIiJSIiIkYxKiYiIiRGMSlGLyIiI0YxRjFGMUYxIiM/RjFGL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvImJyKysrKysrKysrITM5M0duWyUqb0UlKVssW2IjUnFBZV1XNHJkX2RPVXRsJWVsQGAnPUJQYDZbSC1RRVlxWHA6KA==

De fato, esta constante \303\251 80!, como se v\303\252 pela seguinte verifica\303\247\303\243o no Maple.

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

SSV0cnVlRyUqcHJvdGVjdGVkRw==

Todas as derivadas de grau mais alto que o grau do polin\303\264mio ser\303\243o zero, como demonstrado pelo seguinte c\303\241lculo do Maple da LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtSSNtbkdGJDYkUSM4MUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjYvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkEvJSlzdHJldGNoeUdGQS8lKnN5bW1ldHJpY0dGQS8lKGxhcmdlb3BHRkEvJS5tb3ZhYmxlbGltaXRzR0ZBLyUnYWNjZW50R0ZBLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUC1GLDYlUSJvRicvJSdpdGFsaWNHUSV0cnVlRicvRjdRJ2l0YWxpY0YnRjtGNi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0Y2derivada.

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

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2XnAqJCksKCokKUkieEdGKCIiJSIiIkYxKiYiIiRGMSlGLyIiI0YxRjFGMUYxIiM/RjFGL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi9GL0YvRi8iIiE=

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 12.4: <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSNkeEYnRjdGOkY9LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZJLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGPQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSNkeEYnRjdGOkY9LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZJLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGPQ==</Equation> <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUklbXN1cEdGJDYlLUYjNiYtSSNtb0dGJDYtUSIoRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSV0cnVlRicvJSpzZXBhcmF0b3JHUSZmYWxzZUYnLyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRk8tSSZtZnJhY0dGJDYoLUYjNiZGKy1GIzYmLUYsNiVRInhGJy8lJ2l0YWxpY0dGPy9GO1EnaXRhbGljRictRjc2LVEoJm1pbnVzO0YnRjovRj5GQkZAL0ZERkJGRUZHRklGSy9GTlEsMC4yMjIyMjIyZW1GJy9GUUZgby1GLDYlUScmIzk2MDtGJy9GZ25GQkY6RjpGK0Y6LUYjNiZGKy1GIzYnRistRiM2JkYrLUYyNiVGWS1JI21uR0YkNiRRIjJGJ0Y6LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjpGam4tRl9wNiRRIjRGJ0Y6RjpGK0Y6LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZdcS8lKWJldmVsbGVkR0ZCLUY3Ni1RIilGJ0Y6Rj1GQEZDRkVGR0ZJRktGTS9GUVEsMC4xMTExMTExZW1GJ0Y6LUZfcDYkUSI3RidGOkZicEYrRjpGK0Y6">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUklbXN1cEdGJDYlLUYjNiYtSSNtb0dGJDYtUSIoRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSV0cnVlRicvJSpzZXBhcmF0b3JHUSZmYWxzZUYnLyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRk8tSSZtZnJhY0dGJDYoLUYjNiZGKy1GIzYmLUYsNiVRInhGJy8lJ2l0YWxpY0dGPy9GO1EnaXRhbGljRictRjc2LVEoJm1pbnVzO0YnRjovRj5GQkZAL0ZERkJGRUZHRklGSy9GTlEsMC4yMjIyMjIyZW1GJy9GUUZgby1GLDYlUScmIzk2MDtGJy9GZ25GQkY6RjpGK0Y6LUYjNiZGKy1GIzYnRistRiM2JkYrLUYyNiVGWS1JI21uR0YkNiRRIjJGJ0Y6LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjpGam4tRl9wNiRRIjRGJ0Y6RjpGK0Y6LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZdcS8lKWJldmVsbGVkR0ZCLUY3Ni1RIilGJ0Y6Rj1GQEZDRkVGR0ZJRktGTS9GUVEsMC4xMTExMTExZW1GJ0Y6LUZfcDYkUSI3RidGOkZicEYrRjpGK0Y6</Equation> </Text-field>

Existem duas abordagens \303\263bvias para este problema. Esta express\303\243o pode ser diferenciada usando a Regra da Cadeia para derivar o expoente externo e ent\303\243o usando a Regra do Quociente para derivar a express\303\243o racional. Um abordagem alternativa \303\251 reescrever a express\303\243o como o quociente de duas pot\303\252ncias de 7. Com essa abordagem, a Regra do Quociente \303\251 aplicada primeiro e a Regra da Cadeia precisar\303\241 ser aplicada duas vezes -- uma vez para a pot\303\252ncia de 7 no numerador e a outra para a pot\303\252ncia de 7 no denominador.

Preferindo minimizar o n\303\272mero de vezes que a Regra da Cadeia \303\251 aplicada, a primeira abordagem \303\251 adotada aqui, definindo 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 como a fun\303\247\303\243o externa, e 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 como a fun\303\247\303\243o interna, tal que 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. A aplica\303\247\303\243o da regra da cadeia d\303\241:

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYsNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JVEjZHhGJ0Y1RjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkMvJSliZXZlbGxlZEdRJmZhbHNlRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RicvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRkgvJSpzZXBhcmF0b3JHRkgvJSlzdHJldGNoeUdGSC8lKnN5bW1ldHJpY0dGSC8lKGxhcmdlb3BHRkgvJS5tb3ZhYmxlbGltaXRzR0ZILyUnYWNjZW50R0ZILyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGaW4tSShtZmVuY2VkR0YkNiQtRiM2JkYrLUYwNigtRiM2KC1GLDYlUSJ4RidGNUY4RkktRko2LVEoJm1pbnVzO0YnRk1GT0ZRRlNGVUZXRllGZW5GZ25Gam5GSS1GLDYlUSUmcGk7RidGNUY4Rk0tRiM2KUYrLUklbXN1cEdGJDYlRmVvLUkjbW5HRiQ2JFEiMkYnRk0vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRklGaG9GSS1GZHA2JFEiNEYnRk1GTUY+RkFGREZGRitGTUZNRitGTQ==

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERi8=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

A confirma\303\247\303\243o da exatid\303\243o desta resposta pode ser obtida do Maple por:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2JVEjcTRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZTLUYjNiQtSSVtc3VwR0YkNiUtSShtZmVuY2VkR0YkNiQtSSZtZnJhY0dGJDYoLUYjNidGKy1GIzYmLUYsNiVRInhGJ0Y2RjktRj02LVEoJm1pbnVzO0YnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yMjIyMjIyZW1GJy9GVUZmby1GLDYlUScmIzk2MDtGJy9GN0ZERkBGQEYrLyUrZXhlY3V0YWJsZUdGREZALUYjNidGKy1GIzYnRistRiM2JC1GWTYlRl9vLUkjbW5HRiQ2JFEiMkYnRkAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRkBGYm8tRmdwNiRRIjRGJ0ZARkBGK0ZccEZALyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZlcS8lKWJldmVsbGVkR0ZERkAtRmdwNiRRIjdGJ0ZARmpwRkBGK0ZccEZARitGXHBGQC1GPTYtUSI6RidGQEZCRkVGR0ZJRktGTUZPRlFGVEZccEZALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNilGKy1GIzYnLUkmbWZyYWNHRiQ2KC1GIzYlLUkjbW9HRiQ2L1ErJlBhcnRpYWxEO0YnLyUrZm9yZWdyb3VuZEdRLlsxNDQsMTQ0LDE0NF1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvSSttc2VtYW50aWNzR0YkUSZpbmVydEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZJLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlgvJStleGVjdXRhYmxlR0ZJRkEtRiM2J0YrLUYjNiZGOi1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRkJRJ2l0YWxpY0YnRmVuRkFGK0ZlbkZBLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zoby8lKWJldmVsbGVkR0ZJLUY7Ni1RMSZJbnZpc2libGVUaW1lcztGJ0ZBRkdGSkZMRk5GUEZSRlRGVkZZLUYsNiVRI3E0RidGXm9GYW9GZW5GQS1GOzYtUSI9RidGQUZHRkpGTEZORlBGUkZUL0ZXUSwwLjI3Nzc3NzhlbUYnL0ZaRmdwLUYjNictRiw2JVEpc2ltcGxpZnlGJ0Zeb0Zhby1GOzYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZBRkdGSkZMRk5GUEZSRlRGVkZZLUkobWZlbmNlZEdGJDYkLUYjNidGKy1GIzYnLUY2NigtRiM2JS1GOzYtRj1GQUZHRkpGTEZORlBGUkZURlZGWUZlbkZBLUYjNidGKy1GIzYmRlxyRltvRmVuRkFGK0ZlbkZBRmNvRmZvRmlvRltwRl1wRmBwRmVuRkFGK0ZlbkZBRkFGZW5GQUYrRmVuRkFGK0ZlbkZBRitGZW5GQQ==

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JComKSwmSSJ4R0YoIiIiSSNQaUdGJiEiIiIiKEYuKSwmKiQpRi0iIiNGLkYuIiIlRjBGMUYwRi0sJCoqRjFGLiksJkYtRjBGL0YuIiInRi4sKEY0RjBGN0YwKihGNkYuRi1GLkYvRi5GLkYuKUYzIiIpRjBGLg==

Note que esta derivada n\303\243o \303\251 definida quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNidGKy1GIzYmRistSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GP1Enbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGRS1JI21vR0YkNi1RKCZtaW51cztGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZQLyUpc3RyZXRjaHlHRlAvJSpzeW1tZXRyaWNHRlAvJShsYXJnZW9wR0ZQLyUubW92YWJsZWxpbWl0c0dGUC8lJ2FjY2VudEdGUC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmluLUZCNiRRIjRGJ0ZFRkUtRks2LVEiPUYnRkVGTkZRRlNGVUZXRllGZW4vRmhuUSwwLjI3Nzc3NzhlbUYnL0Zbb0Zjby1GQjYkRklGRUZFRitGRQ==, ou seja, onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMkYnRj5GPkYrRj4= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYjNiUtRjs2LVEqJnVtaW51czA7RidGPkZARkNGRUZHRklGS0ZNL0ZQUSYwLjBlbUYnL0ZTRlotSSNtbkdGJDYkUSIyRidGPkY+RitGPkYrRj4=.

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional. In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.

with(RandomTools): randomize(): r1 := Generate(choose([-10..-2,2..10])): n1 := Generate(integer(range=r1)): n2 := Generate(integer(range=2..5)): fn6 := sort(Generate(polynom(integer(range=r1),x,degree=n2)))^n1; ans1 :=sort(diff(fn6,x));

KiQsKCokSSJ4RzYiIiIjIiIlRiVGKCIiKCIiIkYo

LCQqJiwoKiRJInhHNiIiIiMiIiVGJkYpIiIoIiIiIiIkLCZGJiIiKUYpRitGK0Yp

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 12.1</Text-field>

The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component. In the following text region, enter the full contents of the question.

Usando as regras de deriva\303\247\303\243o apropriadas, encontrar a derivada de: f(x) = `$fn6`

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`. Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=ans1;

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0); Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.

evalb(simplify(`$ANSWER`-`$RESPONSE`)=0);

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional. Enter your hints in the following table. You can provide up to three hints.

Use the Chain Rule.

Replace this text with hint 2.

Replace this text with hint 3.

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea2`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Use the Chain Rule.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional. In the following text region, enter feedback to an incorrect response.

Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea2`, `value`); ANSWER := ans1; if evalb(simplify(ANSWER-eval(parse(StudentResponse)))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>7</mn></mrow></mfenced><mn>3</mn></msup><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mrow><mn>8</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>4</mn></mrow></mfenced></mrow></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>7</mn></mrow></mfenced><mn>3</mn></msup><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mrow><mn>8</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>4</mn></mrow></mfenced></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

with(RandomTools): randomize(): nn1 := Generate(integer(range=1..6)): nn2 := Generate(integer(range=1..6)): nn3 := Generate(integer(range=1..30)): fn1 := sort(Generate(polynom(integer(range=1..20),x,degree=nn1)),x): fn2 := sort(Generate(polynom(integer(range=1..20),x,degree=nn2)),x): fn3 := Generate(choose([fn1,fn2,fn1*fn2,fn1/fn2,fn2/fn1])): fn4 := fn3^nn3: fn5 := ``(fn3)^nn3; ans2 := factor(diff(fn4,x));

KiQtSSFHNiI2IyomLDAqJEkieEdGJSIiJyIiJSokRioiIiYiIzkqJEYqRiwiIiIqJEYqIiIkIiIpKiRGKiIiI0YzRioiIz8iIihGMUYxLCxGMCIjPEYyIiM+RjUiIztGKkY7RitGMSEiIkYz

LCQqKCwwKiRJInhHNiIiIiciIiUqJEYmIiImIiM5KiRGJkYpIiIiKiRGJiIiJCIiKSokRiYiIiNGMEYmIiM/IiIoRi5GMyw2ISM4Ri5GJiEkKT1GMiEkPSZGLyEkMypGLSEkcyVGKiIlUTZGJSIkTioqJEYmIiIqIiRPIiokRiZGMSIkbSUqJEYmRjUiJCl5Ri4sLEYtIiM8Ri8iIz5GMiIjO0YmRkdGKEYuISIlRjA=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 12.2</Text-field>

Usando as regras de deriva\303\247\303\243o apropriadas, encontrar a derivada de: f(x) = `$fn5`

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

ans2;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

evalb(simplify(`$ANSWER`-`$RESPONSE`)=0);

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

Use the Chain Rule

Does the Product Rule or Quotient Rule need to be used?

Can your answer be factored?

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Use the Chain Rule</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Does the Product Rule or Quotient Rule need to be used?</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Can your answer be factored?</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea0`, `value`); ANSWER := ans2; if evalb(simplify(ANSWER-eval(parse(StudentResponse)))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>6</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>14</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>5</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><msup><mi>x</mi><mn>4</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>8</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>20</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>7</mn></mrow></mfenced><mn>2</mn></msup><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>13</mn><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>188</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>518</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>908</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>472</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>4</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>1138</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>5</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>935</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>6</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>136</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>9</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>466</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>8</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>788</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>7</mn></msup></mrow></mrow></mfenced></mrow><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>17</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>4</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>19</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>16</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>19</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>6</mn></mrow></mfenced><mn>4</mn></msup></mrow></mfrac></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>6</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>14</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>5</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><msup><mi>x</mi><mn>4</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>8</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>20</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>7</mn></mrow></mfenced><mn>2</mn></msup><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>13</mn><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>188</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>518</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>908</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>472</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>4</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>1138</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>5</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>935</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>6</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>136</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>9</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>466</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>8</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>788</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>7</mn></msup></mrow></mrow></mfenced></mrow><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>17</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>4</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>19</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>16</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>19</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>6</mn></mrow></mfenced><mn>4</mn></msup></mrow></mfrac></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

with(RandomTools): randomize(): n3 := Generate(integer(range=2..4)): n4 := Generate(integer(range=2..4)): fn7 := sort(Generate(polynom(integer(range=-10..10),x,degree=n3)))^n4: n5 := Generate(integer(range=2..4)): n6 := Generate(integer(range=2..4)): while (n6 = n4) do n6 := Generate(integer(range=2..6)) end do: fn8 := sort(Generate(polynom(integer(range=-10..10),x,degree=n5)))^n6: fn9 := Generate(choose([fn7*fn8,fn7/fn8,fn8/fn7,fn8*fn7])); ans3 := factor(diff(fn9,x));

KiYsKiokSSJ4RzYiIiIkIiIpKiRGJSIiIyIiJkYlRighIiYiIiIiIiUsKEYpISIpRiUiIiohIiVGLUYq

LCQqKCwoKiRJInhHNiIiIiMiIilGJiEiKiIiJSIiIkYsLCwqJEYmRisiJDcmKiRGJiIiJCEkayNGJSIkQiNGJiEkOyMiJDQiRixGLCwqRjBGKUYlIiImRiZGKSEiJkYsRjFGKA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 12.3</Text-field>

Usando as regras de deriva\303\247\303\243o apropriadas, encontrar a derivada de: f(x) = `$fn9`

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=ans3;

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

evalb(simplify(`$ANSWER`-`$RESPONSE`)=0);

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

Use the Chain Rule.

Does the Product Rule or Quotient Rule need to be used?

Can your answer be factored?

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Use the Chain Rule.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Does the Product Rule or Quotient Rule need to be used?</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Can your answer be factored?</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea1`, `value`); ANSWER := ans3; if evalb(simplify(ANSWER-eval(parse(StudentResponse)))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mrow><mn>8</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>9</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>4</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mrow><mn>512</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>4</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>264</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>223</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>216</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>109</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>8</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>8</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>5</mn></mrow></mfenced><mn>3</mn></msup></mrow></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mrow><mn>8</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>9</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>4</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mrow><mn>512</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>4</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>264</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>223</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mn>216</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>109</mn></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>8</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>8</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>5</mn></mrow></mfenced><mn>3</mn></msup></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Resumo</Text-field>

Fun\303\247\303\265es formadas pela composi\303\247\303\243o de duas ou mais fun\303\247\303\265es podem ser derivadas pela Regra da Cadeia. A chave para ser capaz de usar a Regra da Cadeia efetivamente \303\251 a identifica\303\247\303\243o das fun\303\247\303\265es envolvidas na composi\303\247\303\243o. A habilidade para reconhecer estas fun\303\247\303\265es \303\251 outra chave no desenvolvimento de sua habilidade de derivar.

Derivadas de ordens superiores s\303\243o definidas pela deriva\303\247\303\243o repetida. Este processo pode ser continuado enquanto a derivada exista. Para polin\303\264mios, foi descoberto que a deriva\303\247\303\243o reduz o grau em um. Em particular, qualquer derivada de ordem mais elevada que o grau do polin\303\264mio ser\303\241 zero. Derivadas de fun\303\247\303\265es racionais e rec\303\255procas de polin\303\264mios- quase nada que requeira o uso da Regra do Quociente para derivar - envolver\303\241 polin\303\264mios de ordens de cada vez mais elevadas no denominador.

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Pr\303\263ximo Cap\303\255tulo</Text-field>

O Tutor M\303\251todos de Diferencia\303\247\303\243o pode ser usado para ajudar a desenvolver a habilidade para determinar a regra de deriva\303\247\303\243o mais apropriada a ser usada a cada passo em um problema de deriva\303\247\303\243o.

Nossa lista de regras de deriva\303\247\303\243o est\303\241 quase completa. O pr\303\263ximo cap\303\255tulo, sobre fun\303\247\303\265es trigonom\303\251tricas, completar\303\241 nossa lista - pelo menos para este curso. Esse cap\303\255tulo tamb\303\251m fornece oportunidades para continuar praticando todas as regras de deriva\303\247\303\243o.

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