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Re: Defining derivatives

• To: mathgroup at smc.vnet.net
• Subject: [mg87959] Re: Defining derivatives
• From: dh <dh at metrohm.ch>
• Date: Mon, 21 Apr 2008 03:26:23 -0400 (EDT)
• References: <fu9vnl$igu$1@smc.vnet.net>

Hi,

thank's a lot for the replies. Here is a short summary of what I just 

learned:

- expressions with the form: f[..][..] are called SubValues of f. 

Documentation of this is non existent, but mathematica knows about it.

- the best way to define derivatives is:

Derivative[1][f]= f2

however, what is still not clear to me is why the following does not work:

Derivative[1][f][x_]= f2[x]

thank's again, Daniel





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];

> 

> Further, where is the information about derivatives stored?

> 

> thank's a lot, Daniel

> 

> 

>