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Beliebt Rechnen >

derivative of sin(xcos^2(x))

Lösung

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

Lösung

- 2 cos (x) + 3 cos^{3} (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

Graph

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