Derivative of Exponential Function

Theorem
Let $\exp$ be the exponential function.

Then:
 * $D_x \left({\exp x}\right) = \exp x$

Proof 2
We use the fact that the exponential function is the inverse of the natural logarithm function:


 * $y = e^x \iff x = \ln y$

Also see

 * Equivalence of Exponential Definitions where it is shown that $D_x \exp x = \exp x$ can be used to define the exponential function.