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

解

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

- \frac{26}{( 3 x - 4 ) ^{2}}

解答ステップ

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

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

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

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

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

簡素化

\frac{5 ( 3 x - 4 ) - 3 ( 5 x + 2 )}{( 3 x - 4 ) ^{2}} : - \frac{26}{( 3 x - 4 ) ^{2}}

= - \frac{26}{( 3 x - 4 ) ^{2}}