derivative f(x)=(e^x)/(4-4x)

解

導関数

f (x) = \frac{e ^{x}}{4 - 4 x}

\frac{e ^{x} ( - x + 2 )}{4 ( x - 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{e ^{x}}{4 - 4 x})

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} ) ( 4 - 4 x ) - \frac{d}{d x} ( 4 - 4 x ) e ^{x}}{( 4 - 4 x ) ^{2}}

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

\frac{d}{d x} (4 - 4 x) = - 4

= \frac{e ^{x} ( 4 - 4 x ) - ( - 4 ) e ^{x}}{( 4 - 4 x ) ^{2}}

簡素化

\frac{e ^{x} ( 4 - 4 x ) - ( - 4 ) e ^{x}}{( 4 - 4 x ) ^{2}} : \frac{e ^{x} ( - x + 2 )}{4 ( x - 1 ) ^{2}}

= \frac{e ^{x} ( - x + 2 )}{4 ( x - 1 ) ^{2}}