derivative of x/(7x+9)

解

\frac{d}{d x} (\frac{x}{7 x + 9})

\frac{9}{( 7 x + 9 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x}{7 x + 9})

商の法則を適用:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (7 x + 9) = 7

= \frac{1 \cdot ( 7 x + 9 ) - 7 x}{( 7 x + 9 ) ^{2}}

簡素化

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