# Derivative of Identity Function/Corollary

## Corollary to Derivative of Identity Function

$\dfrac {\mathrm d} {\mathrm d x} \left({c x}\right) = c$

where $c$ is a constant.

## Proof

 $\displaystyle \frac {\mathrm d} {\mathrm d x} \left({c x}\right)$ $=$ $\displaystyle c \frac {\mathrm d} {\mathrm d x} x$ Derivative of Constant Multiple $\displaystyle$ $=$ $\displaystyle c \times 1$ Derivative of Identity Function $\displaystyle$ $=$ $\displaystyle c$

$\blacksquare$