I am not sure how to do the follow.
$\displaystyle \frac{dy}{dx } (\frac{5\pi }{6 } )$
Can anyone help?
The way that you have stated the question is still unclear. I am assuming you mean
$\displaystyle x=\sqrt{3}\sin(t) \quad y=-\cos(t)$
If this is the cases then
$\displaystyle \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}= \frac{\sin(t)}{\sqrt{3}\cos(t)}=\frac{\tan(t)}{\sq rt{3}}$
Now just evaluate at the given value of t.