derivative of (4x-7/(2x+1))

解

\frac{d}{d x} (\frac{4 x - 7}{2 x + 1})

\frac{18}{( 2 x + 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{4 x - 7}{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} ( 4 x - 7 ) ( 2 x + 1 ) - \frac{d}{d x} ( 2 x + 1 ) ( 4 x - 7 )}{( 2 x + 1 ) ^{2}}

\frac{d}{d x} (4 x - 7) = 4

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

= \frac{4 ( 2 x + 1 ) - 2 ( 4 x - 7 )}{( 2 x + 1 ) ^{2}}

拡張

4 (2 x + 1) - 2 (4 x - 7) : 18

= \frac{18}{( 2 x + 1 ) ^{2}}