What is the derivative of y(x) = e^{5ix} when 5i is a complex number?

[Trenthan]

Hey guys/ girls and thanks in advance

Okay this may seem like the dumbest question on the planet. But i figure i better ask before i waste the lecture's time of booking a consult.

Whats the derivative of

$y(x) = e^{5ix}$

where 5i is a complex number

both the partial and standard derivative would be

$\frac{dy}{dx} =\frac{\partial y}{\partial x} = 5i*e^{5ix}$

In the notes the 'i' is missed at various stages but he arrives at the correct solution which I've verified with other sources. Just the derivation i question... since it uses

$\frac{dy}{dx} =\frac{\partial y}{\partial x} = 5*e^{5ix}$

Any particular reason this could even be true... ? (Im just thinking a big typo but its over many pages so yea...)

Cheers Trent

 

[Hootenanny]

It is most likely a typo. On the other hand, if he is only looking for the imaginary part of the derivative, then his answer is correct.