In Nye p.5 I read:
We sometimes use the symbols $x_1,x_2,x_3$ instead of $Ox_1,Ox_2,Ox_3$ to denote the direction of the axes when no confusion can arise with the coordinates of a point, which are also denoted by $x_1,x_2,x_3$.
This has me wondering, Should axes $Ox_i$ or coordinates of a point $x_i$ be used in notation for gradient? E.g., for scalar $f$, do we write the gradient as, $$\frac{\partial f}{\partial Ox_i}$$ or as, $$\frac{\partial f}{\partial x_i}$$?