system
Given the following post, respond as if you're commenting on Reddit:
human
Why is the derivative of e^x the same as e^x?

It baffles me that the gradient function can be equal to the function itself. Anyone care to shed some light on this?
gpt
First, remember what a derivative is: The "rate of change" (or "slope") of the line/function.

So, at a certain value of x, the function e^x is changing at a rate of e^x (the slope of e^2 at the point x=2 is e^2).

Other functions have this property at a single point:

f(x) = x^2 => f(2) = 4

f'(x) = 2x => f'(2) = 4

e is a special case because this quirk exists long its entire curve.

Also, don't forget that the derivative of e^2x is 2e^2x - only e^x acts as a derivation identity.