derivative y=(7x-1)/(8x+3)

解

導関数

y = \frac{7 x - 1}{8 x + 3}

\frac{29}{( 8 x + 3 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{7 x - 1}{8 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} ( 7 x - 1 ) ( 8 x + 3 ) - \frac{d}{d x} ( 8 x + 3 ) ( 7 x - 1 )}{( 8 x + 3 ) ^{2}}

\frac{d}{d x} (7 x - 1) = 7

\frac{d}{d x} (8 x + 3) = 8

= \frac{7 ( 8 x + 3 ) - 8 ( 7 x - 1 )}{( 8 x + 3 ) ^{2}}

拡張

7 (8 x + 3) - 8 (7 x - 1) : 29

= \frac{29}{( 8 x + 3 ) ^{2}}