Derivative of Hyperbolic Cosine of a x

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Theorem

$\map {\dfrac \d {\d x} } {\cosh a x} = a \sinh a x$


Proof

\(\ds \map {\dfrac \d {\d x} } {\cosh x}\) \(=\) \(\ds \sinh x\) Derivative of $\cosh x$
\(\ds \leadsto \ \ \) \(\ds \map {\dfrac \d {\d x} } {\cosh a x}\) \(=\) \(\ds a \sinh a x\) Derivative of Function of Constant Multiple

$\blacksquare$


Also see