My partial differentiation skills are a bit rusty

[geordief]

From here

https://arxiv.org/pdf/physics/0302045.pdf

Using Eqs. (9) and (10), we obtain
X(x2 + h, t, v) − X(x2, t, v) = X(x1 + h, t, v) − X(x1, t, v). (11)

Dividing both sides by h and taking the limit h → 0, we obtain ∂X /∂x ¦ x2 = ∂X/ ∂x¦ x1

 

I have lost familiarity with the notation and would appreciate a bit of help  if possible.

 

My copy and paste has mangled the form of the expression (which can be seen properly at the link at the top  of the OP.

 

It is the  import of the x subscript1 and x subscript2 in the expression that I am rusty with(if I was ever  up to speed in the first  place -some 30years ago)

 

The  subject of the link itself ,Deriving the velocity addition Law from first principles is of interest to me and I might appreciate any feedback (possibly in another thread) especially as to whether there are any flaws in the document that might mean I am wasting my time trying to go through it.