derivative of (3+x/(1-3x))

解

\frac{d}{d x} (\frac{3 + x}{1 - 3 x})

\frac{10}{( 1 - 3 x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{3 + x}{1 - 3 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} ( 3 + x ) ( 1 - 3 x ) - \frac{d}{d x} ( 1 - 3 x ) ( 3 + x )}{( 1 - 3 x ) ^{2}}

\frac{d}{d x} (3 + x) = 1

\frac{d}{d x} (1 - 3 x) = - 3

= \frac{1 \cdot ( 1 - 3 x ) - ( - 3 ) ( 3 + x )}{( 1 - 3 x ) ^{2}}

簡素化

\frac{1 \cdot ( 1 - 3 x ) - ( - 3 ) ( 3 + x )}{( 1 - 3 x ) ^{2}} : \frac{10}{( 1 - 3 x ) ^{2}}

= \frac{10}{( 1 - 3 x ) ^{2}}