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Beliebt Rechnen >

derivative of e^{ikx}

Lösung

\frac{d}{d x} (e^{ik x})

Lösung

- sin (k x) k + i cos (k x) k

Schritte zur Lösung

\frac{d}{d x} (e^{ik x})

Vereinfache

e^{ik x} : cos (k x) + i sin (k x)

= \frac{d}{d x} (cos (k x) + i sin (k x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (cos (k x)) + \frac{d}{d x} (i sin (k x))

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

\frac{d}{d x} (i sin (k x)) = i cos (k x) k

= - sin (k x) k + i cos (k x) k

Graph

Beliebte Beispiele

derivative of (2x-3^4)

\frac{d}{d x} ((2 x - 3)^{4})

derivative (x^3-1)^{100}

d er i v a t i v e (x^{3} - 1)^{100}

integral of y^{-2/3}

\int y^{- \frac{2}{3}} d y

integral from 0 to pi/2 of 16cos^5(x)

\int_{0}^{\frac{π}{2}} 16 cos^{5} (x) d x

derivative ln(xe^{sqrt(x)}+4)

d er i v a t i v e ln (x e^{x} + 4)