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Guia de Estudo de C\303\241lculo \302\251 Maplesoft, a division of Waterloo Maple Inc., 2005 Cap\303\255tulo 12: A Regra da Cadeia
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field> Uma omiss\303\243o da lista de regras de deriva\303\247\303\243o (differentiation) \303\251 uma regra para derivar a composi\303\247\303\243o de fun\303\247\303\265es (functions). A Regra da Cadeia (Chain Rule) 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 de Deriva\303\247\303\243o Passo-a-Passo (Step-by-Step Differentiation Tutor) 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"><Font encoding="UTF-8">Cap\303\255tulo Gloss\303\241rio</Font></Text-field> Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio de Matem\303\241tica Maple ( Maple Math Dictionary). chainrule composition constant continuous degree denominator derivative differencequotient difference differentiable differentiate differentiation evaluate even exponent factor function limit minimize numerator polynomial exponent productrule product proof quotientrule quotient rationalfunction reciprocal substitution value zero
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Inicializa\303\247\303\243o</Font></Text-field> restart;
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Composi\303\247\303\243o de Fun\303\247\303\265es </Font></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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. Porisso, 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 (value) da fun\303\247\303\243o composta (composite) 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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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictSSNtb0dGJDYuUSRzaW5GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkotRjA2LVEwJkFwcGx5RnVuY3Rpb247RidGNkY5RjxGPkZARkJGREZGRkhGSy1JKG1mZW5jZWRHRiQ2JC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjdRJ2l0YWxpY0YnRjZGK0Y2 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21uR0YkNiRRIjJGJ0Y4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GLDYlUSJ4RicvRjZRJXRydWVGJy9GOVEnaXRhbGljRidGOA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GOVEnbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGPw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSRzaW5GJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RidGNy8lJmZlbmNlR0Y2LyUqc2VwYXJhdG9yR0Y2LyUpc3RyZXRjaHlHRjYvJSpzeW1tZXRyaWNHRjYvJShsYXJnZW9wR0Y2LyUubW92YWJsZWxpbWl0c0dGNi8lJ2FjY2VudEdGNi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RicvRjVRJXRydWVGJy9GOFEnaXRhbGljRidGN0Y3RjdGK0Y3
Tabela 12.1 Fun\303\247\303\265es Compostas 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 e suas partes componentes
(A palavra composition tem somente uma pron\303\272ncia; a palavra composite, duas. Ela \303\251 pronunciada com-POS'-it em USA, e COMP'-o-zit em outros lugares de l\303\255ngua Inglesa.)
<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 cadeiaLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEiLkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0Yv 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUYsNiVRInhGJ0Y2RjlGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZoby1GIzYnLUYsNiVRImZGJ0Y2RjlGPC1GIzYmRlgtRiM2JkYrLUYjNictRiw2JVEiZ0YnRjZGOUY8RlZGK0ZARitGQEZfb0ZARitGQEYrRkBGK0ZA, a composi\303\247\303\243o de f com g, \303\251 diferenci\303\241vel em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ae 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 cadeia(corrente) est\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 (product) 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 (numerator) e denomonador, a real "prova" deste resultado deve ser estabelecida em termos de quocientes da diferen\303\247a difference quotients (onde realmente temos sim fra\303\247\303\243o!). Aqui est\303\241 um esbo\303\247o dessa prova (proof) (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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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERi8=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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiUtRiw2JVEoJkRlbHRhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiw2JVEidUYnL0Y4USV0cnVlRicvRjtRJ2l0YWxpY0YnRjotRiM2JUY0LUYsNiVRInhGJ0ZARkJGOi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGTi8lKWJldmVsbGVkR0Y5RitGOg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERi8=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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUkmbWZyYWNHRiQ2KC1JI21pR0YkNiVRI2R5RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUZNNiVRI2R1RidGUEZTLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Znbi8lKWJldmVsbGVkR0Y0LUZNNiNRIUYnRi8= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYsNiVRI2R1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiVRI2R4RidGNUY4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZDLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRisvRjlRJ25vcm1hbEYn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0ZGLUYsNi1RIidGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUkobWZlbmNlZEdGJDYkLUYjNiQtRko2JVEidUYnRk1GUEYvRi8tRko2JVEiZ0YnRk1GUEZSLUZWNiQtRiM2JC1GSjYlUSJ4RidGTUZQRi9GLy1GSjYjUSFGJ0Yv 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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"><Font encoding="UTF-8">Deriva\303\247\303\243o da Regra da Cadeia </Font></Text-field> Os requerimentos exatos para f e g que fazem LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= diferenci\303\241vel (differentiable) ser\303\243o discutidos mais tarde. Para determinar a derivada (derivative) de F em termos de f, g, e suas derivadas, come\303\247a -se com a defini\303\247\303\243o da derivada, a saber, F := x -> f(g(x)): dq1 := (F(x+h)-F(x)): dF1 := Limit( dq1/h, h=0 ): `F'`(x) = dF1; Ly1JI0YnRzYiNiNJInhHRiUtSSZMaW1pdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYsJi1JImZHRiU2Iy1JImdHRiU2IywmRiciIiJJImhHRiVGN0Y3LUYxNiMtRjRGJiEiIkY3RjhGPC9GOCIiIQ== Assumindo que g \303\251 diferenci\303\241vel em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, ent\303\243o g deve ser cont\303\255nua (continuous) 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 (substitution) no quociente da diferen\303\247a (difference quotient) pela defini\303\247\303\243o de 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 resulta: q1 := g(x+h) = g(x)+`g'`(x)*h: dq2 := eval( dq1, q1 ): dF2 := Limit( dq2/h, h=0 ): `F'`(x) = dF2; Ly1JI0YnRzYiNiNJInhHRiUtSSZMaW1pdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYsJi1JImZHRiU2IywmLUkiZ0dGJUYmIiIiKiYtSSNnJ0dGJUYmRjZJImhHRiVGNkY2RjYtRjE2I0Y0ISIiRjZGOkY9L0Y6IiIh Este limite (limit) pode ser levado a uma forma que seja reconhec\303\255vel como uma derivada se fizermos q2 := r = `g'`(x)*h: q2; L0kickc2IiomLUkjZydHRiQ2I0kieEdGJCIiIkkiaEdGJEYq Com esta substitui\303\247\303\243o podemos escrever dF3a := eval( dq2/h, isolate(q2,h) ): dF3 := Limit( dF3a, h=0 ): `F'`(x) = dF3; Ly1JI0YnRzYiNiNJInhHRiUtSSZMaW1pdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKigsJi1JImZHRiU2IywmLUkiZ0dGJUYmIiIiSSJyR0YlRjZGNi1GMTYjRjQhIiJGNkY3RjotSSNnJ0dGJUYmRjYvSSJoR0YlIiIh Isto parece promissor. Porque 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 \303\251 uma constante (constant) com respeito ao limite em h, e \303\251 finito, pode ser fatorado fora factored out 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 dF4 := subs(h=r, dF3): `F'`(x) = dF4; Ly1JI0YnRzYiNiNJInhHRiUtSSZMaW1pdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKigsJi1JImZHRiU2IywmLUkiZ0dGJUYmIiIiSSJyR0YlRjZGNi1GMTYjRjQhIiJGNkY3RjotSSNnJ0dGJUYmRjYvRjciIiE= ent\303\243o retira o fator (factor) 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, obtendo dF5 := simplify(dF4): `F'`(x) = dF5; Ly1JI0YnRzYiNiNJInhHRiUqJi1JI2cnR0YlRiYiIiItSSZMaW1pdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYsJi1JImZHRiU2IywmLUkiZ0dGJUYmRitJInJHRiVGK0YrLUY1NiNGOCEiIkYrRjpGPS9GOiIiIUYr O limite que resta agora pode ser identificado como a derivada de f, avaliada (evaluated) 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEjRidGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUy1GIzYmLUY9Ni1RIihGJ0ZAL0ZDRjhGRS9GSEY4RklGS0ZNRk8vRlJRLDAuMTY2NjY2N2VtRicvRlVGaG4tRiM2JC1GLDYlUSJ4RidGNkY5RkAtRj02LVEiKUYnRkBGZW5GRUZmbkZJRktGTUZPRmduL0ZVUSwwLjExMTExMTFlbUYnRkBGK0ZALUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjc3Nzc3OGVtRicvRlVGaG8tRiM2KEYrLUYjNictRiw2JVEkZn4nRidGNkY5RjwtRiM2JkZYLUYjNiZGKy1GIzYnLUYsNiVRImdGJ0Y2RjlGPEZWRitGQEYrRkBGX29GQEYrRkAtRj02LVExJkludmlzaWJsZVRpbWVzO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlQtRiM2Jy1GLDYlUSNnJ0YnRjZGOUY8RlZGK0ZARitGQEYrRkBGK0ZA Se o Maple for solicitado para avaliar o limite restante, ele escrever\303\241 o resultado como dF6 := value(dF5): `F'`(x) = dF6; 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 dF7 := convert(dF6,diff): `F'`(x) = dF7; LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjLy1JI0YnR0YmNiNJInhHRiYqJi1JI2cnR0YmRi0iIiItSSVldmFsRyUqcHJvdGVjdGVkRzYkLUklZGlmZkdGNTYkLUkiZkdGJjYjSSN0MUdGJkY9PCMvRj0tSSJnR0YmRi1GMkYp A simplifica\303\247\303\243o que podemos extrair do Maple \303\251 `F'`(x) = subs(t1=tau, dF7); LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjLy1JI0YnR0YmNiNJInhHRiYqJi1JI2cnR0YmRi0iIiItSSVldmFsRyUqcHJvdGVjdGVkRzYkLUklZGlmZkdGNTYkLUkiZkdGJjYjSSR0YXVHRiZGPTwjL0Y9LUkiZ0dGJkYtRjJGKQ==
<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 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pode ser reconhecida como a composi\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtRiM2Ji1GOzYtUSIoRidGPi9GQUY2RkMvRkZGNkZHRklGS0ZNL0ZQUSwwLjE2NjY2NjdlbUYnL0ZTRmZuLUYjNiZGKy1GIzYnLUYsNiVRImdGJ0Y0RjdGOi1GIzYmRlYtRiM2JC1GLDYlUSJ4RidGNEY3Rj4tRjs2LVEiKUYnRj5GWUZDRlpGR0ZJRktGTUZlbi9GU1EsMC4xMTExMTExZW1GJ0Y+RitGPkYrRj5GZm9GPkYrRj5GK0Y+se 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 e 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. Pela Regra da Cadeia, a derivada 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 \303\251 dada por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGL0YyRjlGOS1GLDYjUSFGJ0Y5 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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 (Differentiation Rules) . Maple tamb\303\251m confirma este resultado via q1 := (x^4+3*x^2+1)^2: Diff( q1, x ) = factor( diff(q1,x) );
<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 s\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 (product rule). A computa\303\247\303\243o desta derivada usando a Regra da Cadeia (Chain Rule) \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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. Pela Regra da Cadeia, a derivada 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 \303\251 dada por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGL0YyRjlGOS1GLDYjUSFGJ0Y5 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYtUSgmcHJpbWU7RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjExMTExMTFlbUYnRkQtSShtZmVuY2VkR0YkNiQtRiM2Jy1GSjYjUSFGJ0Zmbi1GIzYmLUZKNiVRImdGJ0ZNRlAtRiw2LVEwJkFwcGx5RnVuY3Rpb247RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GWDYkLUYjNiQtRko2JVEieEYnRk1GUEYvRi9GL0ZmbkYvRi8tRko2JkZdb0ZNLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJ0ZQLUYsNi1RIidGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERmFvRmZuLUYjNiRGZm5GL0ZmbkZmbkYv 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
Exatamente o mesmo resultado \303\251 obtido no Maple via q2 := (x^4+3*x^2+1)^20: Diff( q2, x ) = diff(q2,x); 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 q2a := (x^4+3*x^2+1)^n: Diff( q2a, x ) = simplify( diff(q2a,x) ); 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEkRicnRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlMtRiM2Ji1GPTYtUSIoRidGQC9GQ0Y4RkUvRkhGOEZJRktGTUZPL0ZSUSwwLjE2NjY2NjdlbUYnL0ZVRmhuLUYjNiQtRiw2JVEieEYnRjZGOUZALUY9Ni1RIilGJ0ZARmVuRkVGZm5GSUZLRk1GT0Znbi9GVVEsMC4xMTExMTExZW1GJ0ZARitGQC1GPTYtUSI9RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSwwLjI3Nzc3NzhlbUYnL0ZVRmhvLUYjNihGKy1JJm1mcmFjR0YkNigtRiM2JkYrLUklbXN1cEdGJDYlLUY9Ni1RMCZEaWZmZXJlbnRpYWxEO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlQtSSNtbkdGJDYkUSIyRidGQC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0ZALUYjNiZGKy1GIzYmRmRwLUZicDYlRlxvRmdwRltxRitGQEYrRkAvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmlxLyUpYmV2ZWxsZWRHRkQtRj02LVExJkludmlzaWJsZVRpbWVzO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlQtRiM2Jy1GLDYlUSJGRidGNkY5RjxGVkYrRkBGK0ZARitGQEYrRkA= 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 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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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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERi8=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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERi8=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
A segunda derivada, computada diretamente no Maple, da fun\303\247\303\243o composta \303\251 q3 := (x^4+3*x^2+1)^20: Diff( q3, x$2 ) = factor( diff(q3,x$2) ); Note que a terceira, quarta, quinta e qualquer derivada de ordem mais alta pode ser computada de modo similar, mas as computa\303\247\303\265es se tornar\303\243o cada vez mais complexas, como podem ser vistas nos seguintes c\303\241lculos do Maple. for i from 3 to 6 do Diff( q3, x$i ) = factor( diff(q3,x$i) ) end do; Mais adiante, note que a deriva\303\247\303\243o reduz o grau (degree) de um polin\303\264mio (polynomial) 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 via Diff( q3, x$80 ) = diff( q3, x$80 ); De fato, esta constante \303\251 80!, como se v\303\252 pela seguinte verifica\303\247\303\243o no Maple. evalb( diff(q3,x$80) = 80! ); 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtSSNtbkdGJDYkUSM4MUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjYvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkEvJSlzdHJldGNoeUdGQS8lKnN5bW1ldHJpY0dGQS8lKGxhcmdlb3BHRkEvJS5tb3ZhYmxlbGltaXRzR0ZBLyUnYWNjZW50R0ZBLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUC1GLDYlUSJvRicvJSdpdGFsaWNHUSV0cnVlRicvRjdRJ2l0YWxpY0YnRjtGNi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0Y2 derivada. Diff( q3, x$81 ) = diff( q3, x$81 );
<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="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">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</Equation> </Text-field> Existem duas abordagens \303\263bvias para este problema. Esta express\303\243o pode ser derivada (differentiated) usando a Regra da Cadeia para derivar o expoente externo e ent\303\243o usando a Regra do quociente (Quotient Rule) para derivar a express\303\243o racional (rational). Um aabordagem 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 (denominator). 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGL0YyRjlGOS1GLDYjUSFGJ0Y5 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUYjNiktSSNtbkdGJDYkUSI3RidGL0ZGLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GTDYkUSI2RidGLy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRlM2I1EhRictSShtZmVuY2VkR0YkNiQtRiM2JC1GUzYlUSJ4RidGVkZZRi9GL0Zbb0YvRltvRi8= 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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 via q4 := ( (x-Pi)/(x^2-4) )^7: Diff( q4, x ) = simplify( diff( q4, x ) ); Note que esta derivada n\303\243o \303\251 definida quando 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, i.e., onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMkYnRj5GPkYrRj4= e 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.
Quest\303\243o 12.1 Usando a regra apropriada da derivada, encontrar a derivada de: 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 Quest\303\243o 12.2 Usando a regra apropriada da derivada, encontrar a derivada de: 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 Quest\303\243o 12.3 Usando a regra apropriada da derivada, encontrar a derivada de: 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
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Cap\303\255tulo Resumo</Font></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 exista a derivada. Para polin\303\264mios, foi descoberto que a deriva\303\247\303\243o reduz o grau de 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!!! (reciprocals) de polin\303\264mios- quase nada que almost anything that requeira o uso da Regra do Quociente para derivar - envolver\303\241 polin\303\264mios de ordens de cada vez mais elevadas no denominador. Higher-order derivatives are defined by repeated differentiation. This process can be continued so long as the derivatives exist. For polynomials, it was discovered that differentiation reduces the degree by one. In particular, any derivative of order higher than the degree of the polynomial will be zero. Derivatives of rational functions and reciprocals of polynomials - almost anything that requires use of the Quotient Rule to differentiate - will involve higher and higher order polynomials in the denominator.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Qual \303\251 o Pr\303\263ximo?</Font></Text-field> O Tutor de Deriva\303\247\303\243o Passo-a-Passo 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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