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Beliebt Rechnen >

derivative of (2cos(x)^2)

Lösung

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

Lösung

- 4 sin (2 x)

Schritte zur Lösung

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

Vereinfache

(2 cos (x))^{2} : 4 cos^{2} (x)

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

= 2 cos (x) \frac{d}{d x} (cos (x))

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

= 4 \cdot 2 cos (x) (- sin (x))

Vereinfache

4 \cdot 2 cos (x) (- sin (x)) : - 4 sin (2 x)

= - 4 sin (2 x)

Graph

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