derivative of (2-3x/(7-x))

解

\frac{d}{d x} (\frac{2 - 3 x}{7 - x})

- \frac{19}{( 7 - x ) ^{2}}

解答ステップ

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

\frac{d}{d x} (2 - 3 x) = - 3

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

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

簡素化

\frac{( - 3 ) ( 7 - x ) - ( - 1 ) ( 2 - 3 x )}{( 7 - x ) ^{2}} : - \frac{19}{( 7 - x ) ^{2}}

= - \frac{19}{( 7 - x ) ^{2}}