derivative of (e^x/(5x^2+8))

解

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 8})

\frac{e ^{x} ( 5 x ^{2} + 8 ) - 10 x e ^{x}}{( 5 x ^{2} + 8 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 8})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 5 x ^{2} + 8 ) - \frac{d}{d x} ( 5 x ^{2} + 8 ) e ^{x}}{( 5 x ^{2} + 8 ) ^{2}}

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

\frac{d}{d x} (5 x^{2} + 8) = 10 x

= \frac{e ^{x} ( 5 x ^{2} + 8 ) - 10 x e ^{x}}{( 5 x ^{2} + 8 ) ^{2}}