Taylor Expansion of f+df About x?

Main Question or Discussion Point

How would one expand f+df about x? I'm messing something up in the process and can't seem to resolve it lol

mfb
Mentor
What does f+df mean?
How are they related to x?

There is way too much context missing to answer that.

It shouldn't matter; f is a function of x (and other variables)...

pwsnafu
It shouldn't matter; f is a function of x (and other variables)...
You can't Taylor expand around a variable. You expand around a fixed base point. That's why we write the polynomials terms as ##(x-a)^n##, i.e. expand around a.

mfb
Mentor
It shouldn't matter;
It does matter. Letters without any definition are pointless.
It is like asking "what is x+y?" You cannot answer it (apart from "it is x+y") if you have no idea what x and y are.

Wow...

I was either communicating poorly or something. I found my answer.

f+df = f +(df/dx)dx + (d2f/dx2)dx2 + ... [The parenthetical terms are partials but not the differentials.]

My favorite is, "It does matter. Letters without any definition are pointless." And to think I wasted all that time learning Algebra! :/