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Re: bug? f'[x]'

• To: mathgroup at smc.vnet.net
• Subject: [mg90911] Re: [mg90894] bug? f'[x]'
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 29 Jul 2008 01:39:07 -0400 (EDT)
• References: <200807281153.HAA20595@smc.vnet.net>

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

• References:
  • bug? f'[x]'
    • From: Benjamin.R.Lewis@gmail.com