1. The problem statement, all variables and given/known data So using standard spherical polar co-ordinates, my notes define a sphere as r(s,t) = aCos(s)Sin(t) i + aSin(s)Sin(t) j + aCos(t) k and the normal to the surface is given by the cross product of the two partial differentials: [itex]\partial[/itex]r[itex]/\partial[/itex]s X [itex]\partial[/itex]r[itex]/dt[/itex] So my issue is what is in my notes where: [itex]\partial[/itex]r[itex]/\partial s[/itex]= -aSin(s)Sin(t) i + aCos(s)Sin(t) j + aCot(t) k It is the final part that I don't understand. Why is the partial differential of Cos(t) with respect to s Cot(t)? I would have calculated it as zero. 2. Relevant equations [itex]\partial[/itex][itex]/[/itex][itex]\partial[/itex]s (aCos(t)) = aCot(t) ??? 3. The attempt at a solution All I can think is that it's using a trig identity? As I understand it the k component should only depend upon t, not just from the above equations but in spherical polar co-ordinates in general, at least how I'm picturing it. Thanks in advance for any help.