sleventh

Hello all,
I understand the fact that the principles
LaTeX Code: F= \\nabla \\phi .

LaTeX Code: \\nabla \\times F = 0 .

must apply in order for a force field to be conservative however what i dont get is why showing:

LaTeX Code: f_y= g_x, f_z= h_x, g_z= h_y
where subscripts are what you are taking the derivative with respect to.

is a means to prove the above laws are in effect. i assume it has to do with the fact that subtracting the partial derivatives will give you zero. thank you very much for any help

sleventh