① is incorrect

The condition says that the local Δy=2Δx+o(Δx) of x=a, that is, when x=a, dy=2dx. The writing method should be standardized

, and dy=AΔx or dy=f' (x)Δx in the book is not standardized either.

It should be written as Dy = f'. 1.

Δx and Δy are increments, and dx and dy are differentials. As for what a differential is, it's quite wordy to make it clear. You can temporarily understand it in the limit form of increments, and the differential is just an infinitesimal mark.