Calculate the flux of the vector field out through the surface of (cylinder coordinates).

I've almost solved this problem using the divergence theorem, but I need to calculate the flux through the above sphere when the radius is (because of the singularity along the z-axis).

The problem is that I don't know how to get the normal vector. I know it's , but I'm not quite sure how to get and .

Does anyone have a good online resource for some extra reading by the way?