Assign derivative but evaluate later

Question

I want to re-express the variable z and p in the following form:

func = (z + p)+(z*p)^3+ z^3+ p^2 /.z-> Dx*Exp[x*z+y*p]/.p-> Dy*Exp[x*z+y*p]

where Dx and Dy are the derivative acting on x and y. Now by integrating and manipulating func, I want to explicitly take the derivative Dx and Dy like D[Exp[..],x] and setting x->0 and y->0.

Can somebody help me out how to do this

Answer 1

func = ((z + p) + (z*p)^3 + z^3 + p^2 /. 
  {z -> HoldForm[D[Exp[x*z + y*p], x]]}) /. 
    {p -> HoldForm[D[Exp[x*z + y*p], y]]}

(* evaluate derivatives *)
evderiv = ReleaseHold //@ func

(* result: E^(p y + x z) p + E^(2 p y + 2 x z) p^2 + 
 E^(E^(p y + x z) p y + x z) (z + E^(p y + x z) p y z) + 
 E^(3 E^(p y + x z) p y + 3 x z) (z + E^(p y + x z) p y z)^3 + 
 E^(3 p y + 3 E^(p y + x z) p y + 6 x z)
   p^3 (z + E^(p y + x z) p y z)^3 *)

evderiv /. {x -> 0, y -> 0}

(* result: p + p^2 + z + z^3 + p^3 z^3 *)