derivative g(x)=(5+2x)/(7-8x)

解

導関数

g (x) = \frac{5 + 2 x}{7 - 8 x}

\frac{54}{( 7 - 8 x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{5 + 2 x}{7 - 8 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} ( 5 + 2 x ) ( 7 - 8 x ) - \frac{d}{d x} ( 7 - 8 x ) ( 5 + 2 x )}{( 7 - 8 x ) ^{2}}

\frac{d}{d x} (5 + 2 x) = 2

\frac{d}{d x} (7 - 8 x) = - 8

= \frac{2 ( 7 - 8 x ) - ( - 8 ) ( 5 + 2 x )}{( 7 - 8 x ) ^{2}}

簡素化

\frac{2 ( 7 - 8 x ) - ( - 8 ) ( 5 + 2 x )}{( 7 - 8 x ) ^{2}} : \frac{54}{( 7 - 8 x ) ^{2}}

= \frac{54}{( 7 - 8 x ) ^{2}}