derivative of (1+6x/(9-4x))

解

\frac{d}{d x} (\frac{1 + 6 x}{9 - 4 x})

\frac{58}{( 9 - 4 x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{1 + 6 x}{9 - 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} ( 1 + 6 x ) ( 9 - 4 x ) - \frac{d}{d x} ( 9 - 4 x ) ( 1 + 6 x )}{( 9 - 4 x ) ^{2}}

\frac{d}{d x} (1 + 6 x) = 6

\frac{d}{d x} (9 - 4 x) = - 4

= \frac{6 ( 9 - 4 x ) - ( - 4 ) ( 1 + 6 x )}{( 9 - 4 x ) ^{2}}

簡素化

\frac{6 ( 9 - 4 x ) - ( - 4 ) ( 1 + 6 x )}{( 9 - 4 x ) ^{2}} : \frac{58}{( 9 - 4 x ) ^{2}}

= \frac{58}{( 9 - 4 x ) ^{2}}