Is there an easy way to hide output function arguments?

Question

I'm working with a bunch of funtions with multiple aguments, say f[x,y,z], g[x,y,z], etc. I want to do operations with them like derivatives and products, and I want to read the result easily, without having to see all the arguments.

Is there an easy way to achive this?

Answer 1

$Version

(* "13.3.1 for Mac OS X ARM (64-bit) (July 24, 2023)" *)

ClearAll["Global`*"]

Use Format

(Format[#[_Symbol, _Symbol, _Symbol]] := #) & /@ {f, g};

(Format[Derivative[n__][#][_Symbol, _Symbol, _Symbol]] := 
     Superscript[#, StringForm["(``,``,``)", n]]) & /@ {f, g};

f[x, y, z]*D[f[x, y, z], x] + 
 g[x, y, z]*D[f[x, y, z], x, {y, 2}]*D[g[x, y, z], z]^2