(\partial)/(\partial u(v))((e^v)/(u(v)+v^2))

解答

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

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

求解步骤

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

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

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

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

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

\int \frac{x ^{2} - 2}{x - 1} d x

\frac{d x}{d t} = k + x r

d er i v a t i v e f (x) = x^{2} cos^{4} (x)

\int 4 t^{3} d t

\int \frac{x ^{2} - 1}{( x ^{3} + x )} d x