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

解答

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

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

求解步骤

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

将

x

视为常数

使用连锁律:

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}})

化简

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

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