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

解

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

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

解答ステップ

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

y, z

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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