Answer
$f'(4)=16$
Work Step by Step
Given, $f(x)=\sqrt x g(x), g(4)=8, \&g'(4)=7.$ Differentiating $f$ with respect to $x$, keeping chain rule as well as product rule in mind,
$$f'(x)=\frac{1}{2\sqrt x}g(x)+\sqrt x g'(x)$$At $x=4$,
$$f'(4)=\frac{1}{2\sqrt4}g(4)+\sqrt 4 g'(4)=\frac{8}{4}+2\times7$$
$$f'(4)=2+14=16.$$