Determine partial / partial x e partial / partial y :
z=f(x y)

Passo 1

Temos z = f(xy). O conteúdo aqui é derivada parcial e aplicação da regra da cadeia: vamos definir u = xy e usar
partial zpartial x = f'(u),partial upartial x
e
partial zpartial y = f'(u),partial upartial y .

Passo 2

Para calcular partial zpartial x , observamos que
partial upartial x = partial (xy)partial x = y .
Aplicando a regra da cadeia:
partial zpartial x = f'(u),partial upartial x = f'(xy),y

Passo 3

Para calcular partial zpartial y , observamos que
partial upartial y = partial (xy)partial y = x .
Aplicando a regra da cadeia:
partial zpartial y = f'(u),partial upartial y = f'(xy),x

Resposta

partial zpartial x = y,f'(xy) partial zpartial y = x,f'(xy)

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