derivative of (6x-1/(4x+3))

解

\frac{d}{d x} (\frac{6 x - 1}{4 x + 3})

\frac{22}{( 4 x + 3 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{6 x - 1}{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} ( 6 x - 1 ) ( 4 x + 3 ) - \frac{d}{d x} ( 4 x + 3 ) ( 6 x - 1 )}{( 4 x + 3 ) ^{2}}

\frac{d}{d x} (6 x - 1) = 6

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

= \frac{6 ( 4 x + 3 ) - 4 ( 6 x - 1 )}{( 4 x + 3 ) ^{2}}

拡張

6 (4 x + 3) - 4 (6 x - 1) : 22

= \frac{22}{( 4 x + 3 ) ^{2}}