derivative of 4cos^3(x-3cos(x))

Lösung

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

12 sin^{3} (x) - 9 sin (x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (4 cos^{3} (x)) = - 12 cos^{2} (x) sin (x)

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

= - 12 cos^{2} (x) sin (x) - (- 3 sin (x))

Vereinfache

- 12 cos^{2} (x) sin (x) - (- 3 sin (x)) : 12 sin^{3} (x) - 9 sin (x)

= 12 sin^{3} (x) - 9 sin (x)

y = 3 (2)^{x}

f (x) = 4^{- 2}

f (x) = (\frac{1}{8})^{x}

f (x) = e^{2 x} + e^{x}

f (x) = 5^{x - 2}