A particle is moving along a hyberbola xy = 12. As it reaches the point (6,2), the y-coordinate is decreasing at a rate of 3sm/s. How fast is the x-coordinate of the point changing at that instant?

Answer 1

The strategy for a problem like this is first to see whether you can write x as a function of y. If you can do that (you can) and you simply differentiate both sides and apply the chain rule, for instance noting that d/dt (ln y) = y^-1dy/dt, you can substitute in your known values of x and y, and dy/dt, and arrive at the answer. Otherwise, you can use implicit differentiation to arrive at the same conclusion.

Translating the problem is important: e.g. "the change in the x-coordinate" simply means dx/dt.