[mg90912] Re: [mg90894] bug? f'[x]'

[Andrzej Kozlowski <akoz at 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
>