d/(dt)(e^{3it})

Lösung

\frac{d}{d t} (e^{3 i t})

- sin (3 t) \cdot 3 + i cos (3 t) \cdot 3

Schritte zur Lösung

\frac{d}{d t} (e^{3 i t})

Vereinfache

e^{3 i t} : cos (3 t) + i sin (3 t)

= \frac{d}{d t} (cos (3 t) + i sin (3 t))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d t} (cos (3 t)) + \frac{d}{d t} (i sin (3 t))

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

\frac{d}{d t} (i sin (3 t)) = i cos (3 t) \cdot 3

= - sin (3 t) \cdot 3 + i cos (3 t) \cdot 3

\int \frac{x ^{3}}{x ^{2} - 100} d x

n = 1 \sum \infty \frac{2}{n ^{2} + 4 n + 2}

\frac{d}{d x} (\frac{sin ( 5 x )}{cos ( 6 x )})

\frac{d}{d x} ((x^{2} - 4)^{2} (x - 1))

d er i v a t i v e \frac{( 1 - 5 t )}{2 + t}