Answer
$\sqrt 3$
Work Step by Step
$\dfrac{dy}{dx}=\dfrac{dy/d \theta }{dx/d \theta }\\=\dfrac{r \cos \theta+\sin\theta \dfrac{dr}{ d \theta}}{- r \sin \theta+\cos\theta \dfrac{dr}{ d \theta}}$
Now,
$\dfrac{dy}{dx}=\dfrac{(1) \cos (\dfrac{\pi}{6})+\sin (\pi/6) (\sqrt 3)}{(-1) \sin (\dfrac{\pi}{6})+\cos (\pi/6) (\sqrt 3) }\\=\dfrac{r \cos \theta+\sin\theta \dfrac{dr}{ d \theta}}{- r \sin \theta+\cos\theta \dfrac{dr}{ d \theta}}\\=\dfrac{\dfrac{\sqrt 3}{2}+\dfrac{1}{2} \times \sqrt 3}{-\dfrac{1}{2}+\dfrac{\sqrt 3}{2} \times \sqrt 3}\\=\sqrt 3$
