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

解

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

- \frac{e ^{\frac{x}{y}} x}{y ^{2}}

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

e^{\frac{x}{y}} (- \frac{x}{y ^{2}}) : - \frac{e ^{\frac{x}{y}} x}{y ^{2}}

= - \frac{e ^{\frac{x}{y}} x}{y ^{2}}