derivative of-1/(x^2-7/x)

解

\frac{d}{d x} (- \frac{1}{x ^{2}} - \frac{7}{x})

\frac{2}{x ^{3}} + \frac{7}{x ^{2}}

解答ステップ

\frac{d}{d x} (- \frac{1}{x ^{2}} - \frac{7}{x})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (\frac{1}{x ^{2}}) - \frac{d}{d x} (\frac{7}{x})

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

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

= - (- \frac{2}{x ^{3}}) - (- \frac{7}{x ^{2}})

簡素化

= \frac{2}{x ^{3}} + \frac{7}{x ^{2}}