derivative of (2x-6/(4-x))

解

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

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

解答ステップ

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

\frac{d}{d x} (2 x - 6) = 2

\frac{d}{d x} (4 - x) = - 1

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

簡素化

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

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