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Beliebt Rechnen >

derivative of cos(xx^{-2})

Lösung

\frac{d}{d x} (cos (x) x^{- 2})

Lösung

- \frac{sin ( x )}{x ^{2}} - \frac{2 cos ( x )}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (cos (x) x^{- 2})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x), g = x^{- 2}

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

= (- sin (x)) x^{- 2} + (- \frac{2}{x ^{3}}) cos (x)

Vereinfache

(- sin (x)) x^{- 2} + (- \frac{2}{x ^{3}}) cos (x) : - \frac{sin ( x )}{x ^{2}} - \frac{2 cos ( x )}{x ^{3}}

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

Graph

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