1. The problem statement, all variables and given/known data Hi PhysicsForums, I am calculating something related to the spheroidal membrane and want to ask you a question. I consider a oblate spheroid (Oblate spheroidal coordinates can also be considered as a limiting case of ellipsoidal coordinates in which the two largest semi-axes are equal in length.) In spheroidal coordinate, the relationship to Cartesian coordinates is [tex]x=a\sqrt((1+u^2) (1-v^2))\cos(\phi)[/tex] [tex]y=a\sqrt((1+u^2) (1-v^2))\sin(\phi)[/tex] [tex]z=a u v[/tex] Now, I want to know how to achieve the normal derivative to the surface of a spheroid (u = const), in terms of the derivatives of u, v and [tex]\phi[/tex]. 2. Relevant equations 3. The attempt at a solution I firstly think that the normal derivative in this case is the partial derivative to u. Because in limit cases (v =1,-1) this lead to the derivative to z. Thank you very much.