derivative (4+x)/(1-4x)

解

導関数

\frac{4 + x}{1 - 4 x}

\frac{17}{( 1 - 4 x ) ^{2}}

解答ステップ

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

\frac{d}{d x} (4 + x) = 1

\frac{d}{d x} (1 - 4 x) = - 4

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

簡素化

\frac{1 \cdot ( 1 - 4 x ) - ( - 4 ) ( 4 + x )}{( 1 - 4 x ) ^{2}} : \frac{17}{( 1 - 4 x ) ^{2}}

= \frac{17}{( 1 - 4 x ) ^{2}}