How do I compute the normal vector to a surface with FEM
 

I am trying to compute the normal vector to an inclined plate with the FEM.
Based on theory, the normal vector is given by

n=(-dz/dx,0,1)

This is the normal to the top surface. There is no variation in the y-direction. Consider it as a 2D geometry. The plate has length L, and height H, and it is inclined with a slope equal to PHI, so that it's bottom right corner is located at (a,0) and it's top left corner is located at (b,1).

If I use the FEM to compute the dz/dx derivative, I will find that it is equal to zero. Does this make sense?
The only way to compute a non-zero value for the dz/dx derivative is to solve the problem where the domain was originally a rectangular which deformed to the one I have now. Is this the only way to compute the normal vector with FEM?

I am trying to calculate the normal on the outer surface of a circle. The circle lies in the y-z plane.

I compute the value of the derivative dz/dy (which is equal to (y-y0)/(z-z0), if the equation for the circle is (z-z0)^2+(y-y0)^2=R^2 ), and there is no good agreement between FEM and theory.
Any ideas why this is happening?

My mistake, I can not compute the normal vectors because both x and z are independent variables.

So, how do I calculate the normal vectors in a moving boundary domain.
If we assume that x=f(X,Z) and z=h(X,Z) taking the derivative of dx/dZ will give me the rate of deformation. But, we need to compute quantities such as dx/dz.

Does anybody has any idea about how to compute the normal vectors with FEM?