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

解

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

- sin (x) + i cos (x)

解答ステップ

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

簡素化

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

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

和/差の法則を適用:

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

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

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

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

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