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

解

導関数

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

\frac{10}{( 3 - 4 x ) ^{2}}

解答ステップ

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

簡素化

\frac{2 ( 3 - 4 x ) - ( - 4 ) ( 1 + 2 x )}{( 3 - 4 x ) ^{2}} : \frac{10}{( 3 - 4 x ) ^{2}}

= \frac{10}{( 3 - 4 x ) ^{2}}