# Math Help - about rates

Suppose a particle is moving along a path described by g(x)=x^2/((x-4)^2). At the point (3,9), the X-coordinate of the particle is decreasing at a rate of 2.4cm/s. At what rate is the y-coordinate of the particle changing?

2. You have y=x^2/(x-4)^2

Rewrite as y(x-4)^2=x^2

Now, differentiate implicitly wrt time.

2y(x-4)x'+[(x-4)^2]y'=2xx'

Solve for y' and we get:

y'=[(2x-2xy+8y)/(x-4)^2]*x'

Now, enter in x, y, and x' and find y'

Remember, x' is decreasing so it is -2.4