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

解

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

\frac{e ^{\frac{y}{z}} x}{z}

解答ステップ

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

x, z

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

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

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

\frac{\partial}{\partial y} (\frac{y}{z}) = \frac{1}{z}

= x e^{\frac{y}{z}} \frac{1}{z}

簡素化

x e^{\frac{y}{z}} \frac{1}{z} : \frac{e ^{\frac{y}{z}} x}{z}

= \frac{e ^{\frac{y}{z}} x}{z}