Derivadas Conforme j\303\241 foi explicado na parte introdut\303\263ria, para o Maple existe uma distin\303\247\303\243o entre uma express\303\243o alg\303\251brica e uma fun\303\247\303\243o . Por exemplo,

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Derivamos uma express\303\243o expr em rela\303\247\303\243o \303\240 vari\303\241vel x com o comando diff( expr, vari\303\241vel) O retorno do comando diff \303\251 uma express\303\243o (n\303\243o uma fun\303\247\303\243o). O comando diff( F ,x ) = [Maple Math] calcula a derivada parcial da express\303\243o F em rela\303\247\303\243o \303\240 vari\303\241vel x . Por exemplo

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calcula a derivada de Ep em rela\303\247\303\243o \303\240 vari\303\241vel a Dada uma fun\303\247\303\243o f ent\303\243o derivamos esta fun\303\247\303\243o com o operador D cujo argumento s\303\263 pode ser uma fun\303\247\303\243o D(fun\303\247\303\243o) O retorno do operador D \303\251 uma fun\303\247\303\243o. Por exemplo, dada a fun\303\247\303\243o quadr\303\241tica acima

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Observamos que n\303\243o se pode colocar a vari\303\241vel dependente (x) dentro do argumento do operador D . Veja como o Maple responde ao exemplo abaixo

As fun\303\247\303\265es seno e cosseno s\303\243o definidas no Maple por sin e cos , deste modo

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A derivada parcial de ordem superior de uma express\303\243o \303\251 dada por diff( express\303\243o, var1, var2, var3,...)

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Lembramos que dadas duas fun\303\247\303\265es f e g , ent\303\243o f@g denota a fun\303\247\303\243o composta f(g(x)). O operador D pode calcular a regra da cadeia formalmente, sem que estas fun\303\247\303\265es sejam definidas

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Os comandos diff e D podem ser usados com repeti\303\247\303\243o de n vezes com diff(express\303\243o, x$n) (D@@n) (f) O retorno \303\251 a derivada n-\303\251sima da express\303\243o ou da fun\303\247\303\243o. Por exemplo

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A derivada parcial de uma express\303\243o pode ser escrita,mas sem executar, com o comando inerte Diff Diff (expr, x, y,..., z) O retorno \303\251 a expess\303\243o matem\303\241tica da opera\303\247\303\243o deriva\303\247\303\243o, por exemplo

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Sintaxe dos comandos utilizados diff( express\303\243o, vari\303\241vel), D(fun\303\247\303\243o), diff( express\303\243o, var1, var2, var3,...), diff(express\303\243o, x$n), (D@@n)(fun\303\247\303\243o), Diff(express\303\243o, x, y, ... , z)