# Derivative of Exponential Function/Corollary 1

## Corollary to Derivative of Exponential Function

Let $\exp x$ be the exponential function.

Let $c \in \R$.

Then:

$D_x \left({\exp \left({c x}\right)}\right) = c \exp \left({c x}\right)$

## Proof

 $\displaystyle \displaystyle D_x \left({\exp \left({c x}\right)}\right)$ $=$ $\displaystyle c D_{c x} \left({\exp \left({c x}\right)}\right)$ Derivative of Function of Constant Multiple $\displaystyle$ $=$ $\displaystyle c \exp \left({c x}\right)$ Derivative of Exponential Function

$\blacksquare$