Answer
$y'=\dfrac{1}{2\sqrt{x}}$
Work Step by Step
Simplify the expression:
$y=\dfrac{x-a}{\sqrt{x}-\sqrt{a}} \times \dfrac{\sqrt{x}+\sqrt{a}}{\sqrt{x}+\sqrt{a}}$
$y=\dfrac{(x-a)(\sqrt{x}+\sqrt{a})}{(x-a)}=\sqrt{x}+\sqrt{a}$
$y=x^{1/2}+a^{1/2}$
Apply power rule:
$y'=\dfrac{1}{2\sqrt{x}}$