gistfile1.txt

Clear[Grad, Jac, InvJacGrad, ChangeVariable];
Grad[f_, args_] := Module[{IdM},
  IdM = IdentityMatrix[Length[args]];
  Evaluate[Derivative[Sequence @@ #][f]] @@ args & /@ IdM
  ]
Jac[yOf_, args_] := Module[{IdM},
  IdM = IdentityMatrix[Length[args]];
  Transpose[
   Outer[Derivative[Sequence @@ #][#2] @@ args &, IdM, yOf, 1]]
  ]
InvJacGrad[f_, xOf_, args_, l_] := Module[{ytemp},
  If[Length[l] == 0, f,
   ytemp = Unique[args];
   Function[
    Evaluate[ytemp],
    Evaluate[(
       Transpose[Inverse[Jac[xOf, ytemp]]].Grad[
         InvJacGrad[f, xOf, ytemp, Rest[l]], 
         ytemp](*Inverse Jacobian used!*)
       )[[First[l]]]
     ]]
   ]
  ]
ChangeVariable[f_, args_, xOf_, newArgs_, g_] := Module[{},
  {Derivative[l__][f] @@ args :> Module[{k = List[l]},
     InvJacGrad[g, xOf, newArgs,
       Flatten[ConstantArray[#, k[[#]]] &
         /@ Range[Length[k]]]] @@ newArgs
     ], f @@ args -> g @@ newArgs}
  ]