derivative of (x^3/({f)(x)})

解

\frac{d}{d x} (\frac{x ^{3}}{f ( x )})

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

解答ステップ

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

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

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