derivative of-3cos(2x+pi/3+2)

Lösung

\frac{d}{d x} (- 3 cos (2 x + \frac{π}{3}) + 2)

- 3 (- sin (2 x) - 3 cos (2 x))

Schritte zur Lösung

\frac{d}{d x} (- 3 cos (2 x + \frac{π}{3}) + 2)

Vereinfache

- 3 cos (2 x + \frac{π}{3}) + 2 : - 3 (\frac{1}{2} cos (2 x) - \frac{3}{2} sin (2 x)) + 2

= \frac{d}{d x} (- 3 (\frac{1}{2} cos (2 x) - \frac{3}{2} sin (2 x)) + 2)

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (3 (\frac{1}{2} cos (2 x) - \frac{3}{2} sin (2 x))) + \frac{d}{d x} (2)

\frac{d}{d x} (3 (\frac{1}{2} cos (2 x) - \frac{3}{2} sin (2 x))) = 3 (- sin (2 x) - 3 cos (2 x))

\frac{d}{d x} (2) = 0

= - 3 (- sin (2 x) - 3 cos (2 x)) + 0

Vereinfache

= - 3 (- sin (2 x) - 3 cos (2 x))

h (x) = - 16 x^{2} + 72 x + 40

f (x) = e^{2 x + 3} - e^{4 x + 3} + 2 e^{3}

f (x) = 7 - ∣ x - 1 ∣

y = - 5 x + 24

f (x) = 5 x^{5} - 3 x^{2} + x - 10