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

解

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

\frac{23}{( 4 x + 3 ) ^{2}}

解答ステップ

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

\frac{d}{d x} (5 x - 2) = 5

\frac{d}{d x} (4 x + 3) = 4

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

拡張

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

= \frac{23}{( 4 x + 3 ) ^{2}}