1. ## derivative

I am not sure how to do the follow.

$\displaystyle \frac{dy}{dx } (\frac{5\pi }{6 } )$

Can anyone help?

2. Originally Posted by Arron
I am not sure how to do the follow.

$\displaystyle \frac{dy}{dx } (\frac{5\pi }{6 } )$

Can anyone help?
Do what with it? You have a typo somewhere.

-Dan

3. Basically i am trying to find the gradient of the tangent to an ellipse at the point

with parameter t is$\displaystyle \frac{-cos t}{\sqrt{3}sin t }$,

t = $\displaystyle \frac{5\pi }{6 }$

Can anyone help?

4. Originally Posted by Arron
Basically i am trying to find the gradient of the tangent to an ellipse at the point

with parameter t is$\displaystyle \frac{-cos t}{\sqrt{3}sin t }$,

t = $\displaystyle \frac{5\pi }{6 }$

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.