Well, it's all in the title.
Any help is appreciated!
Are you referring to the derivative of a constant power?
If so, why on earth would they be the same?!?!
The proof of the power rule (at least for positive integers) relies on the binomial theorem, which doesn't have an obvious connection with an/the exponential function.
Maybe have a read of this, then use what you have learnt from here to extend to differentiating using the Chain Rule.
Doesn't that mean that the limit does not exist?
What am I missing.