Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Defining a derivative that distributes for a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64263] Re: Defining a derivative that distributes for a function
  • From: "Sasha P" <mathpro.admin at gmail.com>
  • Date: Wed, 8 Feb 2006 03:54:02 -0500 (EST)
  • References: <ds9mqp$48$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Andreas,

Instead of redefining D operator, consider introducing customized
\[ScriptCapitalD] which you type as "Esc" scD "Esc". Then

In[1]:=
\[ScriptCapitalD][expr_, x__] /; FreeQ[expr, f[_]] := D[expr, x];
\[ScriptCapitalD][expr_, x__] := Module[{t = D[expr, x]},
   t /. {Derivative[n_Integer /; n > 1][f][z_] -> 0} /.
    {Derivative[1][f][z_] :> (1/D[z, x])*f[D[z, x]]}]

In[6]:=
\[ScriptCapitalD][f[x^2] + f[x^4], x]

Out[6]=
f[2*x] + f[4*x^3]

In[7]:=
\[ScriptCapitalD][f[x^2] + f[x^4], {x, 2}]

Out[7]=
f[2] + f[12*x^2]

In[10]:=
\[ScriptCapitalD][f[x^2]*f[x^4], {x, 2}]

Out[10]=
(2/3)*x^2*f[2]*f[12*x^2] + f[x^2]*f[12*x^2] + f[2]*f[x^4]

Hope this is what you aimed at. 

Regards,
Sasha


  • Prev by Date: Problems with With/Block/Module functions
  • Next by Date: DSolve:: Bessel's differential equation
  • Previous by thread: Re: Defining a derivative that distributes for a function
  • Next by thread: Re: Defining a derivative that distributes for a function