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

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