derivative y=(2x+1)/(3x-4)

解

導関数

y = \frac{2 x + 1}{3 x - 4}

- \frac{11}{( 3 x - 4 ) ^{2}}

解答ステップ

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

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

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

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

簡素化

\frac{2 ( 3 x - 4 ) - 3 ( 2 x + 1 )}{( 3 x - 4 ) ^{2}} : - \frac{11}{( 3 x - 4 ) ^{2}}

= - \frac{11}{( 3 x - 4 ) ^{2}}