Think of x and y as x(t) and y(t). They are functions of t. So if you have something like x^2 and you want to take the derivative with respect to t, it would be 2x*(dx/dt). That's where the chain rule comes in.
Use the normal derivative rules like always, just remember to tack on the dx/dt or dy/dt when you differentiate x or y. Once you do that, just treat dy/dt like a normal variable and solve through algebra.