derivative y=(2x-3)/(4x+1)

解

導関数

y = \frac{2 x - 3}{4 x + 1}

\frac{14}{( 4 x + 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{2 x - 3}{4 x + 1})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 2 x - 3 ) ( 4 x + 1 ) - \frac{d}{d x} ( 4 x + 1 ) ( 2 x - 3 )}{( 4 x + 1 ) ^{2}}

\frac{d}{d x} (2 x - 3) = 2

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

= \frac{2 ( 4 x + 1 ) - 4 ( 2 x - 3 )}{( 4 x + 1 ) ^{2}}

拡張

2 (4 x + 1) - 4 (2 x - 3) : 14

= \frac{14}{( 4 x + 1 ) ^{2}}