Derivative of Exponential Function

Theorem
Let $\exp$ be the exponential function.

Then:
 * $\map {\dfrac \d {\d x} } {\exp x} = \exp x$

Also see

 * Equivalence of Definitions of Exponential Function where it is shown that $\dfrac \d {\d x} \exp x = \exp x$ can be used to define the (real) exponential function.