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 $a + b$.

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