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

解

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

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

解答ステップ

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

簡素化

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

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

和/差の法則を適用:

(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