Question

quick question can i take the derivative of e^(z^2) if so is it just 2ze^(z^2)

Answer 1

idk

Answer 2

You first have to establish that the function is analytic in order to be able to apply the chain rule.

This function happens to be analytic because its Taylor series converges for all \(z\) (same as the normal exponential function, \(e^z\)).

Answer 3

(Assuming, of course, that \(z\) is complex. If it is strictly real, then you can take the derivative as you normally would.)