## Calculus 10th Edition

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