Derivative of Cosecant of a x

Corollary to Derivative of Cosecant Function

$\map {\dfrac \d {\d x} } {\csc a x} = -a \csc a x \cot a x$

Proof

\(\ds \map {\dfrac \d {\d x} } {\csc x}\)

\(=\)

\(\ds -\csc x \cot x\)

Derivative of $\csc x$

\(\ds \leadsto \ \ \)

\(\ds \map {\dfrac \d {\d x} } {\csc a x}\)

\(=\)

\(\ds -a \csc a x \cot a x\)

Derivative of Function of Constant Multiple

$\blacksquare$

Also see

• Derivative of $\sin a x$
• Derivative of $\cos a x$

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

• Derivative of $\sec a x$