Is there a way in Mathematica for defining rules for derivatives on undefined functions? For example, I would like to define a rule such that for any function $f(x,y)$, when I take the $x$-derivative it gives me a function $\delta f$:
D[f[x,y],x] -> δf[x,y]
D[g[x,y],x] -> δg[x,y]
etc.
EDIT: I should clarify that I am looking for a rule that could act on functions of any type, so not just $f$, $g$, but any function of $(x,y)$.