Re: Re: Re: Forcing a Derivative

• To: mathgroup at smc.vnet.net
• Subject: [mg50800] Re: [mg50793] Re: [mg50778] Re: Forcing a Derivative
• From: Andrzej Kozlowski <andrzej at akikoz.net>
• Date: Wed, 22 Sep 2004 00:10:58 -0400 (EDT)
• References: <cijej8\$hlp\$1@smc.vnet.net> <200409200139.VAA27554@smc.vnet.net> <200409210749.DAA27779@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```But one does not need to introduce x in f:

f[x_]:=x^3

Derivative[2][f]

6 #1&

No x was needed.

As has been pointed out already a number of times, what is not
implemented by default is the algebra of complex  functions, that is,
if f and g are functions then 2f + 3 g or 5 f*g are not considered by
Mathematica to be functions. One reason for that maybe that in
Mathematica the notion of a "function" is broader than in Mathematics.
In any case the algebras of functions and operators are easy to
implement oneself and this has already been done more than once on this
list.

Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/~andrzej/
http://www.mimuw.edu.pl/~akoz/

On 21 Sep 2004, at 16:49, Murray Eisenberg wrote:

> *This message was transferred with a trial version of CommuniGate(tm)
> Pro*
> Your answer, and those of others, just reinforces my complaint about
> this limitation of Mathematica today.  Why should one have to introduce
> what is, from a modern mathematical point of view, an extraneous extra
> variable, "x"?
>
> A function f is an object; an "expression in x" such as f[x] is quite
> another.  Or at least it should be!
>
> Klaus G wrote:
>
>>> ...
>>> Derivative[2][f * g]
>>> just puts a couple of primes on the product rather than actually
>>> computing the dervative.
>>> Thanks for any insight.
>>> Cheers, Scott
>>
>>
>> Hi,
>>
>> f is NOT f[x], so please try:
>>
>> deriv = D[f[x]*g[x], {x, 2}]
>> Collect[deriv, x]
>>
>> regards
>> Klaus G.
>>
>>
>
> --
> Murray Eisenberg                     murray at math.umass.edu
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower      phone 413 549-1020 (H)
> University of Massachusetts                413 545-2859 (W)
> 710 North Pleasant Street            fax   413 545-1801
> Amherst, MA 01003-9305
>
>

```

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