(\partial)/(\partial x)((z)(zx^2+y^2+xyz))

解答

\frac{\partial}{\partial x} ((z) (z x^{2} + y^{2} + x yz))

z (2 z x + zy)

求解步骤

\frac{\partial}{\partial x} ((z) (z x^{2} + y^{2} + x yz))

将

z, y

视为常数

将常数提出:

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

= z \frac{\partial}{\partial x} (z x^{2} + y^{2} + x yz)

使用微分加减法定则:

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

= z (\frac{\partial}{\partial x} (z x^{2}) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (x yz))

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

\frac{\partial}{\partial x} (y^{2}) = 0

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

= z (2 z x + 0 + zy)

化简

= z (2 z x + zy)

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