(\partial)/(\partial x)((z)(2x+3y)^{10})

解答

\frac{\partial}{\partial x} ((z) (2 x + 3 y)^{10})

20 z (2 x + 3 y)^{9}

求解步骤

\frac{\partial}{\partial x} ((z) (2 x + 3 y)^{10})

将

z, y

视为常数

将常数提出:

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

= z \frac{\partial}{\partial x} ((2 x + 3 y)^{10})

使用连锁律:

10 (2 x + 3 y)^{9} \frac{\partial}{\partial x} (2 x + 3 y)

= 10 (2 x + 3 y)^{9} \frac{\partial}{\partial x} (2 x + 3 y)

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

= z \cdot 10 (2 x + 3 y)^{9} \cdot 2

化简

= 20 z (2 x + 3 y)^{9}

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