[Request] for renaming variables

[Angus]

I tried it the other way around if you want, i.e. I defined F1 in the function app as F1(X)=SIN(X)/X.
Then I decided to do some cas work on that.

Question 1: picking F1 from the vars menu App->Function->Symbolic->F1 places F1 on the cas. It is the same if I typed only F1. Whats the difference between Function.F1:=f and only F1? Why do you see the Function.F1:=f typing and why did CR Haeger use it?

Question 2: I found that either dF1/dx nor dF1/dX worked as Tungdual noticed aswell... Is it explainable? I thought F1 was implied to be a function of some variable X. Or x in the cas? why does dF1(x)/dx do the job? Are all variables converted from upper to lower case when using an APP function (not only restricted to function app) in the case and vice versa?

I'd love to see hands on materials with deeper explanation and many examples, soon!

edit: the fact that dF1(x)/dx works seems to be logical after some thinking. Is it that the cas works with the function F1(X), replaces the -in the cas mode- X with the symbolical 'x' and therefore can calculate the differentiation? But why would the cas not work with capital X on the other hand? I think JoeHorn stated that in the cas all Variables are cas Variables no matter how they are typed in. So an 'X' should be symbolic just as 'x' is so that replacing the X in F1 with the cas 'X' should work? I'm getting confused again...