Answer
$\dfrac{dy}{dx}=\dfrac{\cot{y}}{x}.$
At $(2, \dfrac{\pi}{3})\rightarrow\dfrac{dy}{dx}=\dfrac{\cot{\dfrac{\pi}{3}}}{2}=\dfrac{\sqrt{3}}{6}.$
Work Step by Step
$\dfrac{d}{dx}(x\cos{y})=\dfrac{d}{dx}(1)\rightarrow$
$(\cos{y}-\dfrac{dy}{dx}(x\sin{y}))=0\rightarrow$
$\dfrac{dy}{dx}=\dfrac{\cot{y}}{x}.$
At $(2, \dfrac{\pi}{3})\rightarrow\dfrac{dy}{dx}=\dfrac{\cot{\dfrac{\pi}{3}}}{2}=\dfrac{\sqrt{3}}{6}.$