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Re: Derivative of a function with multiple variables

• To: mathgroup at smc.vnet.net
• Subject: [mg69516] Re: [mg69467] Derivative of a function with multiple variables
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Thu, 14 Sep 2006 06:56:44 -0400 (EDT)
• References: <200609130802.EAA18366@smc.vnet.net>

Adel Elsabbagh 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?
> 

Here is a simple way to obtain the result you want (in version 5.2):

In[23]:=
D[f[x,y,z],{{x,y,z},2}]

Out[23]=
{{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]}}

Carl Woll
Wolfram Research

• References:
  • Derivative of a function with multiple variables
    • From: "Adel Elsabbagh" <aelsabbagh@gmail.com>