derivative (2x-1)/(2x+3)

解

導関数

\frac{2 x - 1}{2 x + 3}

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

解答ステップ

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

\frac{d}{d x} (2 x - 1) = 2

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

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

拡張

2 (2 x + 3) - 2 (2 x - 1) : 8

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