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Beliebt Rechnen >

derivative of 2cos^4(x)

Lösung

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

Lösung

- 8 cos^{3} (x) sin (x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

= - 8 cos^{3} (x) sin (x)

Graph

Beliebte Beispiele

(dy)/(dx)=e^{-a*x}-b*y,y(0)=0

\frac{d y}{d x} = e^{- a \cdot x} - b \cdot y, y (0) = 0

limit as x approaches 10 of 1/((x-10)^2)

x \to 10 lim (\frac{1}{( x - 10 ) ^{2}})

d/(dθ)(r(θ)cos(θ))

\frac{d}{d θ} (r (θ) cos (θ))

derivative f(x)=(6x-4)^4

d er i v a t i v e f (x) = (6 x - 4)^{4}

limit as x approaches infinity of (pi/2-arctan(x))^{1/(ln(x))}

x \to \infty lim ((\frac{π}{2} - arctan (x))^{\frac{1}{l n ( x )}})