Hello, I've been having some trouble getting some notations straight and hence my question. Usually when I see f(x,y) it means to me there is some variable z produced for any combination of x and y in the domain of the function. So, z=x^2+y^2 I imagine as a paraboloid. So z=f(x,y) ...... is a function of three variables with x and y being independent . . . but sometimes I see u=F(x,y,z)=f(x,y)-z . . . all of a sudden it seems as though z has suddenly become independent and there are now four variables. I hope someone can clarify my mishap in reading functions properly or provide me with a source where I can read all various ways functions are written. Thank You... EDIT: Reason why I raised this question. I have a function z=ln(xy^2). 1. First consideration . . . If z=f(x,y) then : F(x,y,z)=f(x,y)-z Hence grad(F)=<1/x,2/y,-1> . . . At point(1,1,0) . . . grad(F)=<1,2,-1> . . . where grad(F) is a vector normal to the surface at that point 2. Second consideration . . . If z=f(x,y) then I can also do . . grad(z)=<1/x,2/y> . . . At point(1,1,0) . . . grad(F)=<1,2> . . . which is also normal to the surface with a rising rate of modulus(<1,2>) So I interpreted the problem in two ways and I had two seemingly similar representations of normal vectors to the curve with one having an extra term that I cannot interpret.