(\partial)/(\partial x)((z)((8x+2y)^4))

解答

\frac{\partial}{\partial x} ((z) ((8 x + 2 y)^{4}))

32 z (8 x + 2 y)^{3}

求解步骤

\frac{\partial}{\partial x} ((z) ((8 x + 2 y)^{4}))

将

z, y

视为常数

将常数提出:

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

= z \frac{\partial}{\partial x} ((8 x + 2 y)^{4})

使用连锁律:

4 (8 x + 2 y)^{3} \frac{\partial}{\partial x} (8 x + 2 y)

= 4 (8 x + 2 y)^{3} \frac{\partial}{\partial x} (8 x + 2 y)

\frac{\partial}{\partial x} (8 x + 2 y) = 8

= z \cdot 4 (8 x + 2 y)^{3} \cdot 8

化简

= 32 z (8 x + 2 y)^{3}

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e x p an d (5 + 93) (- 5 - 10)

s im pl i f y (x + 2) (x - 1)