Derivative of Hyperbolic Cosine of a x

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

$\blacksquare$