(\partial)/(\partial x)((z)(e^z-x^2yz))

解答

\frac{\partial}{\partial x} ((z) (e^{z} - x^{2} yz))

- 2 z^{2} x y

求解步骤

\frac{\partial}{\partial x} ((z) (e^{z} - x^{2} yz))

将

z, y

视为常数

将常数提出:

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

= z \frac{\partial}{\partial x} (e^{z} - x^{2} yz)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (\frac{\partial}{\partial x} (e^{z}) - \frac{\partial}{\partial x} (x^{2} yz))

\frac{\partial}{\partial x} (e^{z}) = 0

\frac{\partial}{\partial x} (x^{2} yz) = 2 zy x

= z (0 - 2 zy x)

化简

z (0 - 2 zy x) : - 2 z^{2} x y

= - 2 z^{2} x y

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