d/(dy)((x)((5x+2y)^8))

解答

\frac{d}{d y} ((x) ((5 x + 2 y)^{8}))

16 x (5 x + 2 y)^{7}

求解步骤

\frac{d}{d y} ((x) ((5 x + 2 y)^{8}))

将

x

视为常数

将常数提出:

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

= x \frac{d}{d y} ((5 x + 2 y)^{8})

使用连锁律:

8 (5 x + 2 y)^{7} \frac{d}{d y} (5 x + 2 y)

= 8 (5 x + 2 y)^{7} \frac{d}{d y} (5 x + 2 y)

\frac{d}{d y} (5 x + 2 y) = 2

= x \cdot 8 (5 x + 2 y)^{7} \cdot 2

化简

= 16 x (5 x + 2 y)^{7}

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