If a point moves on the hyperbola x^2-4y^2=36 in such a way that x-coordinate increases at constant rate of 20 units per second. How fast is the y coordinated changing at point (10,4)?
Differentiating implicitly with respect to t,
2 x dx/dt - 4 y dy/dt = 0
dy/dt = (1/2) (x/y) dx/dt
Plug in x=10, y=4 and dx/dt = 20 and crank out the answer.