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

解

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

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

解答ステップ

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

x, z

を定数として扱う

定数を除去:

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

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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}

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

簡素化

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

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