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Re: Defining derivatives

• To: mathgroup at smc.vnet.net
• Subject: [mg87899] Re: Defining derivatives
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sat, 19 Apr 2008 23:49:23 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <fu9vnl$igu$1@smc.vnet.net>

dh wrote:
> Hello All,
> 
> does anybody know how to define symbolic derivatives. E.g.:
> 
> f[x_]:=f1[x];
> 
> f'[x_]:=f2[x];
> 
> this does not work because f on the lefthand side is evaluated. To 
> 
> prevent this (do not forget to remove f before redefining it):
> 
> f[x_]:=f1[x];
> 
> HoldPattern[f'[x_]]:=f2[x];
> 
> this gives no message, but f'[x] returns f1[x] instead of f2[x].
> 
> The same thinhg happens when you change the sequence of definitions:
> 
> f'[x_]:=f2[x];
> 
> f[x_]:=f1[x];

<snip>

Daniel,

You should use *up values*. You can define them thanks to *UpSet[]* or 
*UpSetDelayed[]*. For instance,

In[1]:= Remove[f]
f[x_] := f1[x]
f'[x] ^:= f2[x]
f'[x]

Out[4]= f2[x]

Best regards,
-- Jean-Marc