derivative (1+8x)/(9-2x)

解

導関数

\frac{1 + 8 x}{9 - 2 x}

\frac{74}{( 9 - 2 x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{1 + 8 x}{9 - 2 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 + 8 x ) ( 9 - 2 x ) - \frac{d}{d x} ( 9 - 2 x ) ( 1 + 8 x )}{( 9 - 2 x ) ^{2}}

\frac{d}{d x} (1 + 8 x) = 8

\frac{d}{d x} (9 - 2 x) = - 2

= \frac{8 ( 9 - 2 x ) - ( - 2 ) ( 1 + 8 x )}{( 9 - 2 x ) ^{2}}

簡素化

\frac{8 ( 9 - 2 x ) - ( - 2 ) ( 1 + 8 x )}{( 9 - 2 x ) ^{2}} : \frac{74}{( 9 - 2 x ) ^{2}}

= \frac{74}{( 9 - 2 x ) ^{2}}