[Koshkin]

I think I get your point, but at the same time I disagree.

1) The differential of a function (at a point), dy, is not notation, it is a concept.

2) The differential of the function y = x, dx, is not, then, a notation, either; and, since the derivative is 1, dx = 1 Δx = Δx = x - x0.

3) You can argue, of course, that using dx instead of Δx in dy = f'(x)dx is "notation," but I think the above shows that it is more than that.