derivative cos(x^{-9})

Lösung

ableitung von

cos (x^{- 9})

\frac{9 sin ( \frac{1}{x ^{9}} )}{x ^{10}}

Schritte zur Lösung

\frac{d}{d x} (cos (x^{- 9}))

Wende die Kettenregel an:

- sin (x^{- 9}) \frac{d}{d x} (x^{- 9})

= - sin (x^{- 9}) \frac{d}{d x} (x^{- 9})

\frac{d}{d x} (x^{- 9}) = - \frac{9}{x ^{10}}

= - sin (x^{- 9}) (- \frac{9}{x ^{10}})

Vereinfache

- sin (x^{- 9}) (- \frac{9}{x ^{10}}) : \frac{9 sin ( \frac{1}{x ^{9}} )}{x ^{10}}

= \frac{9 sin ( \frac{1}{x ^{9}} )}{x ^{10}}

\frac{d}{d x} (3 - \frac{7}{2 x ^{\frac{1}{8}}})

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