Re: Derivative of a function with multiple variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg69510] Re: Derivative of a function with multiple variables*From*: "J Siehler" <jsiehler at gmail.com>*Date*: Thu, 14 Sep 2006 06:56:29 -0400 (EDT)*References*: <ee8grk$itd$1@smc.vnet.net>

Adel Elsabbagh wrote: > Assume I have f = f[x,y,z] > I would like to construct a simple function g[f[x,y,z]] that will > generate the Hessian. i.e. Here is a solution that will work with any number of variables. I struggled with this problem when I was first learning Mathematica; I don't think it's easy to do it correctly and cleanly, though I can hope some clever reply to this thread will teach me better. Hess[f_][x__] := Table[ (Derivative @@ MapAt[(# + 1) &, 0 & /@ Range[Length[{x}]], {{i}, {j}}])[f][x], {i, Length[{x}]}, {j, Length[{x}]}] For example, try: g[x_, y_] := 3x^2*y - y^3; Hess[g][x, y] Hess[g][1, 2] and g[x_, y_, z_] := z*x^2/(1 + y^2) Hess[g][x, y, z] Hess[g][1, 2, 3] You might find this useful, too: Grad[f_][x__] := Table[(Derivative @@ RotateRight[PadLeft[{1}, Length[{x}]], i])[f][x],{i, Length[{x}]}]