Re: Derivative of a function with multiple variables

• To: mathgroup at smc.vnet.net
• Subject: [mg69504] Re: [mg69467] Derivative of a function with multiple variables
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 14 Sep 2006 06:56:12 -0400 (EDT)

```g[expr_, var_:{x,y,z}]:=Outer[D[expr,#1,#2]&,var,var];

g[f[x,y,z]]

{{Derivative[2, 0, 0][f][x, y, z], Derivative[1, 1, 0][f][x, y, z], Derivative[1, 0, 1][f][x, y, z]},
{Derivative[1, 1, 0][f][x, y, z], Derivative[0, 2, 0][f][x, y, z], Derivative[0, 1, 1][f][x, y, z]},
{Derivative[1, 0, 1][f][x, y, z], Derivative[0, 1, 1][f][x, y, z], Derivative[0, 0, 2][f][x, y, z]}}

g[x*y*z]

{{0, z, y}, {z, 0, x}, {y, x, 0}}

Bob Hanlon

---- Adel Elsabbagh <aelsabbagh at gmail.com> wrote:
> Hi all,
>
> I am sure this is easy to many of you
>
> 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.
> g[f[x,y,z]]=
> {{Derivative[2,0,0][f][x,y,z], Derivative[1,1,0][f][x,y,z],
> Derivative[1,0,1][f][x,y,z]},
> {Derivative[1,1,0][f][x,y,z], Derivative[0,2,0][f][x,y,z],
> Derivative[0,1,1][f][x,y,z]},
> {Derivative[1,0,1][f][x,y,z], Derivative[0,1,1][f][x,y,z],
> Derivative[0,0,2][f][x,y,z]}}.
>
> Any help?
>
> --