(\partial)/(\partial x)(x^2(y/x))

解答

\frac{\partial}{\partial x} (x^{2} (\frac{y}{x}))

y

求解步骤

\frac{\partial}{\partial x} (x^{2} (\frac{y}{x}))

化简

x^{2} (\frac{y}{x}) : x y

= \frac{\partial}{\partial x} (x y)

将

y

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (x)

使用常见微分定则:

\frac{\partial}{\partial x} (x) = 1

= y \cdot 1

化简

= y

(f (x) (x)^{g (x)})^{'}

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