Answer
$$\frac{{dy}}{{dx}} = 2 - \frac{{\sinh \sqrt x }}{{2\sqrt x }}$$
Work Step by Step
$$\eqalign{
& y = 2x - \cosh \sqrt x \cr
& {\text{Differentiate}} \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {2x} \right] - \frac{d}{{dx}}\left[ {\cosh \sqrt x } \right] \cr
& {\text{Using theorem 5}}{\text{.8}} \cr
& \frac{{dy}}{{dx}} = 2 - \sinh \sqrt x \frac{d}{{dx}}\left[ {\sqrt x } \right] \cr
& \frac{{dy}}{{dx}} = 2 - \sinh \sqrt x \left( {\frac{1}{{2\sqrt x }}} \right) \cr
& \frac{{dy}}{{dx}} = 2 - \frac{{\sinh \sqrt x }}{{2\sqrt x }} \cr} $$
