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

Lösung

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

- \frac{120}{x ^{6}}

Schritte zur Lösung

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

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

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

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

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

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

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

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

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

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

= - \frac{120}{x ^{6}}

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