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

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SUMMARY

The derivative of the function y(x) = e^{5ix} is definitively calculated as dy/dx = 5i * e^{5ix}. This result is consistent across various sources, confirming the inclusion of the complex number '5i' in the derivative. The discussion raises a potential typo in lecture notes where the 'i' is omitted, leading to the incorrect expression dy/dx = 5 * e^{5ix}. However, if the intent was to find only the imaginary part of the derivative, the simplified form could be considered correct.

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Trenthan
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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
 
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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.
 
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