derivative g(x)=((9+6x)/(7-4x))

解

導関数

g (x) = (\frac{9 + 6 x}{7 - 4 x})

\frac{78}{( 7 - 4 x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{9 + 6 x}{7 - 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} ( 9 + 6 x ) ( 7 - 4 x ) - \frac{d}{d x} ( 7 - 4 x ) ( 9 + 6 x )}{( 7 - 4 x ) ^{2}}

\frac{d}{d x} (9 + 6 x) = 6

\frac{d}{d x} (7 - 4 x) = - 4

= \frac{6 ( 7 - 4 x ) - ( - 4 ) ( 9 + 6 x )}{( 7 - 4 x ) ^{2}}

簡素化

\frac{6 ( 7 - 4 x ) - ( - 4 ) ( 9 + 6 x )}{( 7 - 4 x ) ^{2}} : \frac{78}{( 7 - 4 x ) ^{2}}

= \frac{78}{( 7 - 4 x ) ^{2}}