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

$\blacksquare$

Also see

• Derivative of $\cos a x$

• Derivative of $\tan a x$
• Derivative of $\cot a x$

• Derivative of $\sec a x$
• Derivative of $\csc a x$