derivative of (4x-5/(3x+2))

解

\frac{d}{d x} (\frac{4 x - 5}{3 x + 2})

\frac{23}{( 3 x + 2 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{4 x - 5}{3 x + 2})

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 - 5 ) ( 3 x + 2 ) - \frac{d}{d x} ( 3 x + 2 ) ( 4 x - 5 )}{( 3 x + 2 ) ^{2}}

\frac{d}{d x} (4 x - 5) = 4

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

= \frac{4 ( 3 x + 2 ) - 3 ( 4 x - 5 )}{( 3 x + 2 ) ^{2}}

拡張

4 (3 x + 2) - 3 (4 x - 5) : 23

= \frac{23}{( 3 x + 2 ) ^{2}}