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Beliebt Rechnen >

derivative f(x)=x^{14}cos(x)

Lösung

ableitung von

f (x) = x^{14} cos (x)

Lösung

14 x^{13} cos (x) - x^{14} sin (x)

Schritte zur Lösung

\frac{d}{d x} (x^{14} cos (x))

Wende die Produktregel an:

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

f = x^{14}, g = cos (x)

= \frac{d}{d x} (x^{14}) cos (x) + \frac{d}{d x} (cos (x)) x^{14}

\frac{d}{d x} (x^{14}) = 14 x^{13}

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

= 14 x^{13} cos (x) + (- sin (x)) x^{14}

Vereinfache

= 14 x^{13} cos (x) - x^{14} sin (x)

Graph

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