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

解

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

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

解答ステップ

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{\partial}{\partial x} (u (x) + x^{2}) = \frac{\partial}{\partial x} (u (x)) + 2 x

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