Answer
False
Work Step by Step
By the chain rule $\frac{d}{dx}f(\sqrt x)=\frac{f'(\sqrt x)}{2\sqrt x}$
Consider an example:
Take $f(x)=sinx$ and consider $g(x)=sin\sqrt x$
By the chain rule we have
$g'(x)=\frac{cos(\sqrt x)}{2\sqrt x}\ne \frac{cosx}{2\sqrt x}=\frac{f'(x)}{2\sqrt x}$
Hence, the given statement is false.
