partial derivate of a function of vector variable
in [Mathematica]
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From: atlas shrugger on 25 Mar 2010 05:22 Hi, Let's say have function f of vector variable x. f[x_] := x[[1]]^2 + x[[2]]^2 How to compute partial derivate by x_1? Something like D[f[x], {{x[[1]]}}] does not work. I don't want to rewrite function f as f[x1_,x2_]. Thanks for help.
From: dh on 25 Mar 2010 07:08 Hi, f[x_]:=.. is a function of one argument (even if your scalar is a list) and not a function of several variables. Therefore there are no partial derivatives. The easiest soultion would be to define a function of several variables, but you do not want to do this. Another solution is to "create" a function of several variables on the fly, e.g. using dummy variables like: D[f[{x1,x2},x1]]/.{x1->first argument, x2->second argument} or we may use a pure function like: Derivative[1, 0][Evaluate@f[{#1, #2}] &] or another simpler possibility: Evaluate@D[f[{#1, #2}], #1]& Daniel On 25.03.2010 10:22, atlas shrugger wrote: > Hi, > > Let's say have function f of vector variable x. > f[x_] := x[[1]]^2 + x[[2]]^2 > > How to compute partial derivate by x_1? > Something like D[f[x], {{x[[1]]}}] does not work. > > I don't want to rewrite function f as f[x1_,x2_]. > > Thanks for help. > -- Daniel Huber Metrohm Ltd. Oberdorfstr. 68 CH-9100 Herisau Tel. +41 71 353 8585, Fax +41 71 353 8907 E-Mail:<mailto:dh(a)metrohm.com> Internet:<http://www.metrohm.com>
From: Bob Hanlon on 25 Mar 2010 07:09 f[x_] := x.x x = {x1, x2, x3}; f[x] x1^2 + x2^2 + x3^2 D[f[x], #] & /@ x {2 x1,2 x2,2 x3} D[f[x], x[[1]]] 2 x1 Bob Hanlon ---- atlas shrugger <ashrugger(a)gmail.com> wrote: ============= Hi, Let's say have function f of vector variable x. f[x_] := x[[1]]^2 + x[[2]]^2 How to compute partial derivate by x_1? Something like D[f[x], {{x[[1]]}}] does not work. I don't want to rewrite function f as f[x1_,x2_]. Thanks for help.
From: Vasyl' on 26 Mar 2010 06:38 Many thanks for help. I got that there is advanced level mathematica I need to study :)
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