(\partial)/(\partial y)((z)(3x+5y)^9)

解答

\frac{\partial}{\partial y} ((z) (3 x + 5 y)^{9})

45 z (3 x + 5 y)^{8}

求解步骤

\frac{\partial}{\partial y} ((z) (3 x + 5 y)^{9})

将

z, x

视为常数

将常数提出:

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

= z \frac{\partial}{\partial y} ((3 x + 5 y)^{9})

使用连锁律:

9 (3 x + 5 y)^{8} \frac{\partial}{\partial y} (3 x + 5 y)

= 9 (3 x + 5 y)^{8} \frac{\partial}{\partial y} (3 x + 5 y)

\frac{\partial}{\partial y} (3 x + 5 y) = 5

= z \cdot 9 (3 x + 5 y)^{8} \cdot 5

化简

= 45 z (3 x + 5 y)^{8}

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