Finding the velocity vector

Question

Am I finding the equation of the slope of the tangent line at c(t)?

$\frac{dy/dt}{dx/dt}$ = $\frac{2t}{3t^2-8}$

Answer 1

The position of the particle at any particular time will be given by the vector

r(t) = (x(t),y(t))

You want to differentiate r(t), i.e,

 v(t) = dr(t)/dt = (dx(t)/dt,dy(t)/dt)

Note that the speed will be given by

 s(t) = d/dt of sqrt(x(t)^2+y(t)^2), but that is not the velocity or a vector