# Derivative of Sine Function/Corollary

## Corollary to Derivative of Sine Function

$\map {\dfrac \d {\d x} } {\sin a x} = a \cos a x$

## Proof

 $\ds \map {\dfrac \d {\d x} } {\sin x}$ $=$ $\ds \cos x$ Derivative of $\sin x$ $\ds \leadsto \ \$ $\ds \map {\dfrac \d {\d x} } {\sin a x}$ $=$ $\ds a \cos a x$ Derivative of Function of Constant Multiple

$\blacksquare$