(\partial)/(\partial x)((e^x)/(x^2+10))

解

\frac{\partial}{\partial x} (\frac{e ^{x}}{x ^{2} + 10})

\frac{e ^{x} ( x ^{2} + 10 ) - 2 x e ^{x}}{( x ^{2} + 10 ) ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{e ^{x}}{x ^{2} + 10})

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} ) ( x ^{2} + 10 ) - \frac{\partial}{\partial x} ( x ^{2} + 10 ) e ^{x}}{( x ^{2} + 10 ) ^{2}}

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

\frac{\partial}{\partial x} (x^{2} + 10) = 2 x

= \frac{e ^{x} ( x ^{2} + 10 ) - 2 x e ^{x}}{( x ^{2} + 10 ) ^{2}}