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Re: bug? f'[x]'

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  • Subject: [mg90912] Re: [mg90894] bug? f'[x]'
  • From: Andrzej Kozlowski <akoz at>
  • Date: Tue, 29 Jul 2008 01:39:18 -0400 (EDT)
  • References: <> <>

Perhaps I should have added that this:

  Derivative[m + n][f]

is mathematically perfectly sound, while this:

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 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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