Nested radical differentiation

Calculus Level 3

$y = \sqrt{x+\sqrt{x-\sqrt{x+\sqrt{x-\sqrt{x+\cdots}}}}}$

If $\left. \dfrac{dy}{dx} \right|_{x=3}$ can be represented in the form $\dfrac{a}{b}$ , where $a, b$ are coprime positive integers, find $a + b$ .