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

解答

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

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

求解步骤

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

将

x, y

视为常数

使用指数法则:

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

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

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

使用连锁律:

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

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

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

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

化简

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

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

\frac{d}{d x} (\frac{4 x ^{2} + 3}{2 x - 1})

d er i v a t i v e f (x) = x^{3} + y^{3} = 16

a re a x = 5 - 5 \cdot y^{2}, x = 5 \cdot y^{2} - 5

\frac{d}{d x} (\frac{x ^{4} + 48}{24 x})

in v erse l a pl a ce \frac{e ^{- π s}}{s}