Derivative of Cosine Function/Corollary

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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

$\blacksquare$


Also see