[mg90900] Re: bug? f'[x]'

[Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>]

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