derivative of x/(6-x)

解

\frac{d}{d x} (\frac{x}{6 - x})

\frac{6}{( 6 - x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x}{6 - x})

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} ( 6 - x ) - \frac{d}{d x} ( 6 - x ) x}{( 6 - x ) ^{2}}

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

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

= \frac{1 \cdot ( 6 - x ) - ( - 1 ) x}{( 6 - x ) ^{2}}

簡素化

\frac{1 \cdot ( 6 - x ) - ( - 1 ) x}{( 6 - x ) ^{2}} : \frac{6}{( 6 - x ) ^{2}}

= \frac{6}{( 6 - x ) ^{2}}