(\partial)/(\partial u(v))((e^v)/(u(v)+v^6))

Lösung

\frac{\partial ^{2}}{\partial u ( v ) \partial v} (\frac{e ^{v}}{u ( v ) + v ^{6}})

- \frac{e ^{v} ( v ^{6} + u ( v ) - 2 ( 6 v ^{5} + \frac{\partial}{\partial v} ( u ( v ) ) ) )}{( u ( v ) + v ^{6} ) ^{3}}

Schritte zur Lösung

\frac{\partial ^{2}}{\partial u ( v ) \partial v} (\frac{e ^{v}}{u ( v ) + v ^{6}})

\frac{\partial}{\partial u ( v )} (\frac{e ^{v}}{u ( v ) + v ^{6}}) = - \frac{e ^{v}}{( u ( v ) + v ^{6} ) ^{2}}

= \frac{\partial}{\partial v} (- \frac{e ^{v}}{( u ( v ) + v ^{6} ) ^{2}})

\frac{\partial}{\partial v} (- \frac{e ^{v}}{( u ( v ) + v ^{6} ) ^{2}}) = - \frac{e ^{v} ( v ^{6} + u ( v ) - 2 ( 6 v ^{5} + \frac{\partial}{\partial v} ( u ( v ) ) ) )}{( u ( v ) + v ^{6} ) ^{3}}

= - \frac{e ^{v} ( v ^{6} + u ( v ) - 2 ( 6 v ^{5} + \frac{\partial}{\partial v} ( u ( v ) ) ) )}{( u ( v ) + v ^{6} ) ^{3}}

\frac{d}{d x} (\frac{2}{1 - 2 x})

\frac{\partial}{\partial x} (\frac{x}{2 x ^{2} + y ^{2}})

\int x^{3} \cdot e^{12 x} d x

d er i v a t i v e x^{3} + 3 x^{2}

d er i v a t i v e e^{s i n (2 x)} + sin (e^{2 x})