Alright let's see,
\psi(x,y)=(x,y,f(x,y))
...
\frac{\partial \psi}{\partial x} = [ x/dx , y/dx, f(x,y)/dx] = (1, 0 , f(x,y))
\frac{\partial \psi}{\partial y} = [ x/dy, y/dy, f(x,y)/dy] = (0, 1, f(x,y))
cross those two.
| 1 0 f(x,y)/dx |
| 0 1 f(x,y)/dy |
(0 - f(x,y)/dx)i -...