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Re: bug? f'[x]'
*To*: mathgroup at smc.vnet.net
*Subject*: [mg90900] Re: bug? f'[x]'
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Tue, 29 Jul 2008 01:37:04 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
*References*: <g6kc46$k6f$1@smc.vnet.net>
Benjamin.R.Lewis at gmail.com wrote:
> In[]:= f'[x] =!= f[x]' && f''[x] === f'[x]'
> Out[]= True
>
> Can anyone explain this?
First, keep in mind that Mathematica does *pattern* matching.
Second, SameQ requires exact correspondence between expressions when
those expressions are expressed in *FullForm* (FullForm being the
internal representation used by Mathematica regardless of the type of
input).
In your case, the fullform of f'[x] is Derivative[1][f][x] whereas the
fullform of f[x]' is Derivative[1][f[x]], both expressions are
*syntactically* not the same.
OTOH, the fullform of f''[x] is Derivative[2][f][x] whereas the fullform
of f'[x]' is Derivative[2][f][x], both expressions are *syntactically*
the same. (Note that the fullform of f[x]'' is Derivative[2][f[x]].)
In[1]:= f'[x] =!= f[x]' && f''[x] === f'[x]'
Out[1]= True
In[2]:= f'[x] =!= f[x]'
Out[2]= True
In[3]:= f''[x] === f'[x]'
Out[3]= True
In[4]:= f'[x] // FullForm
Out[4]//FullForm= Derivative[1][f][x]
In[5]:= f[x]' // FullForm
Out[5]//FullForm= Derivative[1][f[x]]
In[6]:= f''[x] // FullForm
Out[6]//FullForm= Derivative[2][f][x]
In[7]:= f'[x]' // FullForm
Out[7]//FullForm= Derivative[2][f][x]
Regards,
-- Jean-Marc
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