(\partial)/(\partial y)(8x^{y/z})

解答

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

\frac{8 x ^{\frac{y}{z}} ln ( x )}{z}

求解步骤

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

将

x, z

视为常数

将常数提出:

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

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

使用指数法则:

a^{b} = e^{b l n (a)}

x^{\frac{y}{z}} = e^{\frac{y}{z} l n (x)}

= 8 \frac{\partial}{\partial y} (e^{\frac{y}{z} l n (x)})

使用连锁律:

e^{\frac{y}{z} l n (x)} \frac{\partial}{\partial y} (\frac{y}{z} ln (x))

= e^{\frac{y}{z} l n (x)} \frac{\partial}{\partial y} (\frac{y}{z} ln (x))

\frac{\partial}{\partial y} (\frac{y}{z} ln (x)) = \frac{ln ( x )}{z}

= 8 e^{\frac{y}{z} l n (x)} \frac{ln ( x )}{z}

化简

8 e^{\frac{y}{z} l n (x)} \frac{ln ( x )}{z} : \frac{8 x ^{\frac{y}{z}} ln ( x )}{z}

= \frac{8 x ^{\frac{y}{z}} ln ( x )}{z}

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