(\partial)/(\partial x)(e^{ikx})

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\int (1 + sin^{2} (x)) d x

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

\int x \cdot x^{2} + 5 d x

t a y l or ln (4 - x)

\frac{\partial}{\partial z} (ln (1 + x^{2} + e^{y} + z))