Answer
$\frac{1}{16}$
Work Step by Step
$\frac{d}{dx}(g(\sqrt x))=g'(\sqrt x)\times\frac{d}{dx}\sqrt x$
$=g'(\sqrt x)\times\frac{1}{2\sqrt x}$
$\frac{d}{dx}(g\sqrt x)|_{x=16}=g'(\sqrt {16})\times\frac{1}{2\sqrt {16}}$
$=g'(4)\times\frac{1}{2\times4}=\frac{1}{2}\times\frac{1}{8}=\frac{1}{16}$
