derivative (x^3)/(3-3x)

解

導関数

\frac{x ^{3}}{3 - 3 x}

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

解答ステップ

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

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

簡素化

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

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