derivative y=(f(x))/(x^7)

解答

导数

y = \frac{f ( x )}{x ^{7}}

\frac{x \frac{df}{d x} - 7 f ( x )}{x ^{8}}

求解步骤

\frac{d}{d x} (\frac{f ( x )}{x ^{7}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{df}{d x} x ^{7} - \frac{d}{d x} ( x ^{7} ) f ( x )}{( x ^{7} ) ^{2}}

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{\frac{df}{d x} x ^{7} - 7 x ^{6} f ( x )}{( x ^{7} ) ^{2}}

化简

\frac{\frac{df}{d x} x ^{7} - 7 x ^{6} f ( x )}{( x ^{7} ) ^{2}} : \frac{x \frac{df}{d x} - 7 f ( x )}{x ^{8}}

= \frac{x \frac{df}{d x} - 7 f ( x )}{x ^{8}}