Thread: Unit Tangent Vector

My professor assigned this problem:

F(x,y) = x / y^2. We had to find the Unit Tangent Vector at the point (2, -2).

I honestly didn't know where to even start with this. I know what to do if I'm given a vector function, but F(x,y) sure isn't one.

I'm just looking for pointers on how to start, after that I should be able to do it on my own.

If it were me, I'd find a Unit Normal and then try to decide what might be wanted. Perhaps the Unit Tangent in the direction of the Gradient?

z= F(x,y) is a surface and there are an infinite number of tangent vectors at any point, filling the tangent plane. If the problem were F(x,y)= constant, that would define, implicitely, a curve in the plane which would have a tangent vector.