Derivative of Hyperbolic Cosine of a x

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Theorem

$D_x \left({\cosh a x}\right) = a \sinh a x$


Proof

\(\displaystyle D_x \left({\cosh x}\right)\) \(=\) \(\displaystyle \sinh x\) Derivative of $\cosh x$
\(\displaystyle \implies \ \ \) \(\displaystyle D_x \left({\cosh a x}\right)\) \(=\) \(\displaystyle a \sinh a x\) Derivative of Function of Constant Multiple

$\blacksquare$


Also see