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

解答

\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}}

求解步骤

\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}}

\frac{d}{d x} (\frac{x}{x ^{2} + 4})

x \to 25 lim (lo g_{5} (x))

\frac{d}{d x} (x^{5} ln (2 x))

d er i v a t i v e f (x) = (\frac{x ^{2}}{x - 1})^{2}

\int_{0}^{1} 1 d x