If xy^2=12 and dy/dt=6, find dx/dt when y=2

[dcgirl16]

If xy^2=12 and dy/dt=6, find dx/dt when y=2

The way i thought to do this would be
(1)(y^2)+x(y)(dy/dt)=0 but i don't know x so this isn't working, what am i doing wrong

 

[Terilien]

You just multiply the derivative of x with respect to y by 6(chain rule). You can find x as a function of y by solving for it so x=12/y^2.