Re: Derivative of a function with multiple variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg69483] Re: Derivative of a function with multiple variables*From*: dh <dh at metrohm.ch>*Date*: Thu, 14 Sep 2006 06:54:52 -0400 (EDT)*References*: <ee8grk$itd$1@smc.vnet.net>

Hi Adel, you nearly got it yourself. Define: 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]}}; SetASttributes[g,HoldFirst]; the last line is necessary to preven evaluation of f. now you could say: f[x_,y_,z_]:=x^4+y^5+z^6; g[f[x,y,z]] and you get back: {{12 x^2, 0, 0}, {0, 20 y^3, 0}, {0, 0, 30 z^4}} Daniel 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? >