# Exponential is Strictly Increasing/Proof 2

## Theorem

The function $\map f x = \exp x$ is strictly increasing.

## Proof

For all $x \in \R$:

 $\ds D_x \exp x$ $=$ $\ds \exp x$ Derivative of Exponential Function $\ds$ $>$ $\ds 0$ Exponential of Real Number is Strictly Positive

Hence the result, from Derivative of Monotone Function.

$\blacksquare$