JSFHJSFHCap\303\255tulo 7-Visualizando Derivadas Direcionais e GradientesComo observamos as derivadas direcionais e os gradientes, parece interessante observar uma visualiza\303\247\303\243o do Maple de tudo o que estamos fazendo.
Primeiro, deseja carregar os comandos apropriados. Vamos precisar de comandos dos pacotes linalg, plottools e plots. (Reiniciar limpa se j\303\241 estivermos executando uma planilha do Maple.)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.1-Derivadas direcionais:
Para preliminares, queremos definir a fun\303\247\303\243o, o ponto no plano x-y em que estamos avaliando e o vetor de dire\303\247\303\243o em que estamos interessados \342\200\213\342\200\213em obter uma derivada.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JSFHEm seguida, gostar\303\255amos de calcular um vetor unit\303\241rio na dire\303\247\303\243o desejada e na coordenada z do ponto de interesse.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JSFH