Derivative of Hyperbolic Cosecant of a x

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Theorem

$\map {\dfrac \d {\d x} } {\csch a x} = -a \csch a x \coth a x$


Proof

\(\ds \map {\dfrac \d {\d x} } {\csch x}\) \(=\) \(\ds -\csch x \coth x\) Derivative of $\csch x$
\(\ds \leadsto \ \ \) \(\ds \map {\dfrac \d {\d x} } {\csch a x}\) \(=\) \(\ds -a \csch a x \coth a x\) Derivative of Function of Constant Multiple

$\blacksquare$


Also see