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Beliebt Rechnen >

derivative of-4cos^3(x)

Lösung

\frac{d}{d x} (- 4 cos^{3} (x))

Lösung

12 cos^{2} (x) sin (x)

Schritte zur Lösung

\frac{d}{d x} (- 4 cos^{3} (x))

Entferne die Konstante:

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

= - 4 \frac{d}{d x} (cos^{3} (x))

Wende die Kettenregel an:

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

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

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

= - 4 \cdot 3 (cos (x))^{2} (- sin (x))

Vereinfache

= 12 cos^{2} (x) sin (x)

Graph

Beliebte Beispiele

limit as x approaches 3 of 4

x \to 3 lim (4)

derivative 15x-0.4x^2-80

d er i v a t i v e 15 x - 0.4 x^{2} - 80

derivative f(x)=cos^6(x)

d er i v a t i v e f (x) = cos^{6} (x)

derivative of 0.5e^{x-1}

\frac{d}{d x} (0.5 e^{x - 1})

derivative 9/(x-7)

d er i v a t i v e \frac{9}{x - 7}