- 2,903

- 13

"In the special case in which the equation of a surface S is of the form z=f(x,y) (that is, S is the graph of a function f of two variables), we can write the equation as

F(x,y,z) = f(x,y) - z = 0

and regard S as a level surface (with k=0) of F. Then

Fx(x0,y0,z0) = fx(x0,y0)

Fy(x0,y0,z0) = fy(x0,y0)

Fz(x0,y0,z0)= -1 "

end quote

I understand his moving z to the other side.

But when the take the derivative W.R.T x, what about the z? z is not a variable, z is a functin of x and y, so why dont u have some dz/dx term in there, Fx(x0,y0,z0)=fx(x0,y0) -dz/dx . How did z no longer become a dependent variable on x and y?