derivative y=(x^6)/(f(x))

解

導関数

y = \frac{x ^{6}}{f ( x )}

\frac{6 x ^{5} f ( x ) - \frac{df}{d x} x ^{6}}{f ( x ) ^{2}}

解答ステップ

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

= \frac{6 x ^{5} f ( x ) - \frac{df}{d x} x ^{6}}{f ( x ) ^{2}}