d/(d{y)}({x}^{({z})/({y)}})

解答

\frac{d}{d y} (x^{\frac{z}{y}})

- \frac{e ^{\frac{l n ( x ) z}{y}} ln ( x ) z}{y ^{2}}

求解步骤

\frac{d}{d y} (x^{\frac{z}{y}})

使用指数法则:

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

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

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

使用连锁律:

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

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

\frac{d}{d y} (\frac{z}{y} ln (x)) = - \frac{ln ( x ) z}{y ^{2}}

= e^{\frac{z}{y} l n (x)} (- \frac{ln ( x ) z}{y ^{2}})

化简

e^{\frac{z}{y} l n (x)} (- \frac{ln ( x ) z}{y ^{2}}) : - \frac{e ^{\frac{l n ( x ) z}{y}} ln ( x ) z}{y ^{2}}

= - \frac{e ^{\frac{l n ( x ) z}{y}} ln ( x ) z}{y ^{2}}

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