derivative f(x)=(e^x)/(8x^2+3)

解

導関数

f (x) = \frac{e ^{x}}{8 x ^{2} + 3}

\frac{e ^{x} ( 8 x ^{2} + 3 ) - 16 x e ^{x}}{( 8 x ^{2} + 3 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{e ^{x}}{8 x ^{2} + 3})

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} ) ( 8 x ^{2} + 3 ) - \frac{d}{d x} ( 8 x ^{2} + 3 ) e ^{x}}{( 8 x ^{2} + 3 ) ^{2}}

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

\frac{d}{d x} (8 x^{2} + 3) = 16 x

= \frac{e ^{x} ( 8 x ^{2} + 3 ) - 16 x e ^{x}}{( 8 x ^{2} + 3 ) ^{2}}