$y=\dfrac{x}{\sqrt{a^2-x^2}}$
$y'=\dfrac{\sqrt{a^2-x^2}-x.\dfrac{(-2x)}{2\sqrt{a^2-x^2}} }{a^2-x^2}$
$=\dfrac{\sqrt{a^2-x^2}+\dfrac{x^2}{\sqrt{a^2-x^2}} }{a^2-x^2}$
$=\dfrac{a^2-x^2+x^2}{(a^2-x^2)\sqrt{a^2-x^2}}$
$=\dfrac{a^2}{(a^2-x^2)\sqrt{a^2-x^2}}$