Question

If Y=(2x^2-2)^(1/2), determine dy/dt when x=6 and dx/dt = -3

Answer 1

you are differentiating the x and the y with respect to t. Which is most likely time in this case, but that doesn't matter.

Answer 2

you are going to have to have a chain rule, not only for (2x^2-2)^(1/2), as it is a inner function of a radical, but the chain rule for x itself, which is (times) dx/dt.
And so will it be for y, multiplying times dy/dt.