Answer
$2\sqrt{a}f'(a)$
Work Step by Step
$$\lim_{x \to a}\frac{f(x)-f(a)}{\sqrt{x}-\sqrt{a}}=\frac{0}{0}$$
Using the l'Hospital's rule it follows:
$$\lim_{x \to a}\frac{f(x)-f(a)}{\sqrt{x}-\sqrt{a}}=\lim_{x \to a}\frac{f'(x)}{\frac{1}{2\sqrt x}}=2\sqrt{a}f'(a)$$
