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Re: bug? f'[x]'
*To*: mathgroup at smc.vnet.net
*Subject*: [mg90912] Re: [mg90894] bug? f'[x]'
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Tue, 29 Jul 2008 01:39:18 -0400 (EDT)
*References*: <200807281153.HAA20595@smc.vnet.net> <344EC9C4-D0D2-4141-855E-DBE283AA7586@mimuw.edu.pl>
Perhaps I should have added that this:
Derivative[n][Derivative[m][f]]
Derivative[m + n][f]
is mathematically perfectly sound, while this:
Derivative[n][Derivative[m][f][x]]
Derivative[m + n][f][x]
cerainly is not. But this does not mean this is necesarily a bug. The
syntax of second input illogical and not documented as anything
meaningful in Mathematica but it returns a "meaningful answer" but
perhaps might do so intentinally. Since, however, it is not documented
(and illogical) it is certianly cannot be regarded as any kind of "bug".
Andrzej Kozlowski
>
> On 28 Jul 2008, at 13:53, Benjamin.R.Lewis at gmail.com wrote:
>
>> G'day,
>>
>> In[]:= f'[x] =!= f[x]' && f''[x] === f'[x]'
>> Out[]= True
>>
>> Can anyone explain this?
>>
>> -Ben
>>
>
> Maybe not exactly explain... but
>
> this is a consequence of the following somewhat strange phenomenon:
>
> FullForm[Derivative[n][Derivative[m][f][x]]]
> FullForm[Derivative[m + n][f][x]]
>
> but not for m=0:
>
> FullForm[Derivative[n][Derivative[0][f][x]]]
> FullForm= FullForm[Derivative[n][f[x]]]
>
> Note that the first output is actually the (m+n)-th derivative of f
> at x, but the second output means (if anything) something completely
> different (n-th derivative of the functon f[x]).
>
> Although the first result may be part of some design, it is
> mathematically just as meaningless as the second. So I would guess
> the "explanation" of the phenomenon you have observed is of the
> "garbage in -> garbage out" kind.
>
> Andrzej Kozlowski
>
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