derivative of 1/(x^4-3/(x^2))

解

\frac{d}{d x} (\frac{1}{x ^{4}} - \frac{3}{x ^{2}})

- \frac{4}{x ^{5}} + \frac{6}{x ^{3}}

解答ステップ

\frac{d}{d x} (\frac{1}{x ^{4}} - \frac{3}{x ^{2}})

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{1}{x ^{4}}) - \frac{d}{d x} (\frac{3}{x ^{2}})

\frac{d}{d x} (\frac{1}{x ^{4}}) = - \frac{4}{x ^{5}}

\frac{d}{d x} (\frac{3}{x ^{2}}) = - \frac{6}{x ^{3}}

= - \frac{4}{x ^{5}} - (- \frac{6}{x ^{3}})

簡素化

= - \frac{4}{x ^{5}} + \frac{6}{x ^{3}}