Derivative of Normal on a Surface

Hello. Any help would be greatly appreciated. I am trying to calculate the mean curvature on a boundary. To do this, I am trying to calculate the dot product of the surface gradient operator and the normal vector. Thus, I need to take derivates like d(nr,r). However, whenever I do this, I only get zeros. Does anyone know how to implement these derivatives?

Another question would be, how do you take the derivative of something with respect to arc length, such as dn/ds?

Thanks in advance!
John