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Re: How to use "Apply" to do differentiation ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114452] Re: How to use "Apply" to do differentiation ?
  • From: Roland Franzius <roland.franzius at uos.de>
  • Date: Sun, 5 Dec 2010 21:48:27 -0500 (EST)
  • References: <idd7ts$nja$1@smc.vnet.net>

Am 04.12.2010 12:16, schrieb Mayasky:
> Something simple yet unbelievable occurred when I use:
>
> Apply[D[#, x]&, x^5]
>
> The output is invariably 1 whether I use x^5 or x^100.
> Also I suggest you to try "Trace" command to see
> the weirdness -- the output is messy if pasted as
> text here.
>
> Finally I have to take a detour and use:
> Nest[D[#, x]&, x^5, 1]
>
> I have been using Mathematica for several years and
> never found that. I myself is wordless, but can anyone
> explain that?
>

Its very easy to trace unexpected evaluation results

Trace[D[#, x] & @@ (x^5)] // FullForm

FullForm[{HoldForm[(D[#1, x] & ) @@ (x^5)],
    HoldForm[(D[#1, x] & )[x, 5]], HoldForm[D[x, x]], HoldForm[1]}]

which is the correct formal answer, because Power[x,5] is a function of 
two variables.

Of cause, one can doubt, if an automatic application rule for 
diffentiating sequences of variables without any function head is a 
useful concept.

It is comparable to a concept of differentiating tensor products of 
spaces with respect to position by replacing a factor space V at 
position i in V_1 \times ... \times V_i \times ... by the 
one-dimensional spaces of multiples of the field unit 1.

-- 

Roland Franzius


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