derivative of (x-6/(3-4x))

解

\frac{d}{d x} (\frac{x - 6}{3 - 4 x})

- \frac{21}{( 3 - 4 x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x - 6}{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} ( x - 6 ) ( 3 - 4 x ) - \frac{d}{d x} ( 3 - 4 x ) ( x - 6 )}{( 3 - 4 x ) ^{2}}

\frac{d}{d x} (x - 6) = 1

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

= \frac{1 \cdot ( 3 - 4 x ) - ( - 4 ) ( x - 6 )}{( 3 - 4 x ) ^{2}}

簡素化

\frac{1 \cdot ( 3 - 4 x ) - ( - 4 ) ( x - 6 )}{( 3 - 4 x ) ^{2}} : - \frac{21}{( 3 - 4 x ) ^{2}}

= - \frac{21}{( 3 - 4 x ) ^{2}}