(d^5)/(dx^5)(1/(x^2))

解

\frac{d ^{5}}{d x ^{5}} (\frac{1}{x ^{2}})

- \frac{720}{x ^{7}}

解答ステップ

\frac{d ^{5}}{d x ^{5}} (\frac{1}{x ^{2}})

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

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

\frac{d}{d x} (- \frac{2}{x ^{3}}) = \frac{6}{x ^{4}}

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

\frac{d}{d x} (\frac{6}{x ^{4}}) = - \frac{24}{x ^{5}}

= \frac{d ^{2}}{d x ^{2}} (- \frac{24}{x ^{5}})

\frac{d}{d x} (- \frac{24}{x ^{5}}) = \frac{120}{x ^{6}}

= \frac{d}{d x} (\frac{120}{x ^{6}})

\frac{d}{d x} (\frac{120}{x ^{6}}) = - \frac{720}{x ^{7}}

= - \frac{720}{x ^{7}}