# Derivative of Cosine Function/Corollary

## Corollary to Derivative of Cosine Function

$D_x \left({\cos a x}\right) = -a \sin a x$

## Proof

 $\displaystyle D_x \left({\cos x}\right)$ $=$ $\displaystyle - \sin x$ Derivative of $\cos x$ $\displaystyle \implies \ \$ $\displaystyle D_x \left({\cos a x}\right)$ $=$ $\displaystyle - a \sin a x$ Derivative of Function of Constant Multiple

$\blacksquare$