(\partial)/(\partial u(v))((e^v)/(u(v)+v^5))

解

\frac{\partial ^{2}}{\partial u ( v ) \partial v} (\frac{e ^{v}}{u ( v ) + v ^{5}})

- \frac{e ^{v} ( v ^{5} + u ( v ) - 2 ( 5 v ^{4} + \frac{\partial}{\partial v} ( u ( v ) ) ) )}{( u ( v ) + v ^{5} ) ^{3}}

解答ステップ

\frac{\partial ^{2}}{\partial u ( v ) \partial v} (\frac{e ^{v}}{u ( v ) + v ^{5}})

\frac{\partial}{\partial u ( v )} (\frac{e ^{v}}{u ( v ) + v ^{5}}) = - \frac{e ^{v}}{( u ( v ) + v ^{5} ) ^{2}}

= \frac{\partial}{\partial v} (- \frac{e ^{v}}{( u ( v ) + v ^{5} ) ^{2}})

\frac{\partial}{\partial v} (- \frac{e ^{v}}{( u ( v ) + v ^{5} ) ^{2}}) = - \frac{e ^{v} ( v ^{5} + u ( v ) - 2 ( 5 v ^{4} + \frac{\partial}{\partial v} ( u ( v ) ) ) )}{( u ( v ) + v ^{5} ) ^{3}}

= - \frac{e ^{v} ( v ^{5} + u ( v ) - 2 ( 5 v ^{4} + \frac{\partial}{\partial v} ( u ( v ) ) ) )}{( u ( v ) + v ^{5} ) ^{3}}