Derivative of Hyperbolic Sine of a x

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Theorem

$\map {D_x} {\sinh a x} = a \cosh a x$


Proof

\(\displaystyle \map {D_x} {\sinh x}\) \(=\) \(\displaystyle \cosh x\) Derivative of $\sinh x$
\(\displaystyle \leadsto \ \ \) \(\displaystyle \map {D_x} {\sinh a x}\) \(=\) \(\displaystyle a \cosh a x\) Derivative of Function of Constant Multiple

$\blacksquare$


Also see