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

解

導関数

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

\frac{7}{( 2 x + 1 ) ^{2}}

解答ステップ

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

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

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

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

拡張

3 (2 x + 1) - 2 (3 x - 2) : 7

= \frac{7}{( 2 x + 1 ) ^{2}}