A potential energy function for a two-dimensional force is of the form U = 3 x2y - 6 x. Find the force that acts at the point (x, y). (Use x and y as appropriate.)

Answer 1

I would do it as a vector..

Force=dU/di,j,k = (6xy-6)i + 3x^2 j
where i, j are unit x,y vectors.