I was given the equation z = x^2 - y^2 and was told to find the surface element for the surface z = x^2 - y^2 in polar coordinates. So far I have converted the equation to polar with
z = r^2 cos(theta)^2 - r^2 sin(theta)^2.
I simplified that to
r^2(2cos(theta)^2 - 1) = z
Now i think the next step would be to get 2 none parallel vectors to take the cross product of to find the surface element. I am not entirely sure though which directions I need to do them in. Would I take one holding r constant and one holding theta constant? I don't have a a lot of experience with surface integrals or polar coordinates so this has been a bit confusing and any help would be greatly appreciated.