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Find $ \left. \cfrac{dy}{dx} \right|_{x=\cfrac{\pi}{3}}$ when $y=\cfrac{x}{\cot x}$.

A

$\cfrac{3\sqrt{3}+\pi}{3}$

B

$\cfrac{3 \sqrt{3}+4\pi}{3}$

C

$-\cfrac{3\sqrt{3}+\pi}{3}$

D

$-\cfrac{3 \sqrt{3}+4\pi}{3}$

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