derivative (-5x-9)/(2x+8)

解

導関数

\frac{- 5 x - 9}{2 x + 8}

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

解答ステップ

\frac{d}{d x} (\frac{- 5 x - 9}{2 x + 8})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( - 5 x - 9 ) ( 2 x + 8 ) - \frac{d}{d x} ( 2 x + 8 ) ( - 5 x - 9 )}{( 2 x + 8 ) ^{2}}

\frac{d}{d x} (- 5 x - 9) = - 5

\frac{d}{d x} (2 x + 8) = 2

= \frac{( - 5 ) ( 2 x + 8 ) - 2 ( - 5 x - 9 )}{( 2 x + 8 ) ^{2}}

簡素化

\frac{( - 5 ) ( 2 x + 8 ) - 2 ( - 5 x - 9 )}{( 2 x + 8 ) ^{2}} : - \frac{11}{2 ( x + 4 ) ^{2}}

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