Calc III type question: gradients, normal vectors, and the like

I like the cut of your jib Ring, but would you mind explaining a little more detail of what you did? Specifically, what’s f? I would have imagined that f[sub]z[/sub] = 2z.

Achernar, I couldn’t possibly have been so stupid as to put that minus sign in there. It must have been someone else. Please help me track this malefactor down, a person this moronic shouldn’t be allowed to consume scarce planetary resources.

(God, it’s so sad – I’m such a lamebrain)