(* Differentiation with explanation *)
(* (C) Alexander Frolkin 2001 *)
(* alexander@frolkin.demon.co.uk *)

BeginPackage["EDiff`"]

(* Set attributes *)
(* SetAttributes[EDiff, HoldAll] *)

(* Brief description *)
EDiff::usage := "EDiff[f, x] gives the derivative of f with respect to
x, explaining what is is doing."

(* A few standard derivatives *)
EDiff[a_, x_] := (Print[Constant]; 0) /; FreeQ[a, x]
EDiff[x_, x_] := (Print[Diffx]; 1)
EDiff[x_^n_, x_] := (Print[Power]; n x^(n-1)) /; FreeQ[n, x]
EDiff[Log[x_], x_] := (Print[Log]; 1/x)
EDiff[Sin[x_], x_] := (Print[Sin]; Cos[x])
EDiff[Cos[x_], x_] := (Print[Cos]; -Sin[x])
        (* Separate rule for E^x isn't needed - it's handled by
           Logdiff :-) *)

(* Differentiation rules *)
EDiff[f_ g_, x_] := (Print[Product]; f EDiff[g, x] + g EDiff[f, x])
EDiff[f_/g_, x_] := (Print[Quotient]; (g EDiff[f, x] - f EDiff[g, x])/g^2)
EDiff[f_[g_], x_] := (Print[Chain]; EDiff[f[g], g] EDiff[g, x])
EDiff[f_^g_, x_] := (Print[Logdiff]; f^g EDiff[g Log[f], x])

EndPackage[ ]