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Re: Derivative of a function with multiple variables


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?
> 
> -- 
> Adel Elsabbagh
> 


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