Re: Re: Derivative of a function with multiple variables

• To: mathgroup at smc.vnet.net
• Subject: [mg69545] Re: [mg69504] Re: [mg69467] Derivative of a function with multiple variables
• From: "Adel Elsabbagh" <aelsabbagh at gmail.com>
• Date: Fri, 15 Sep 2006 06:45:13 -0400 (EDT)
• References: <200609141056.GAA21549@smc.vnet.net>

```Thanks all!
Very great help.

On 9/14/06, Bob Hanlon <hanlonr at cox.net> wrote:
> 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?
> >
> > --
> >
>
>

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