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MathGroup Archive 2000

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Re: RE:? D[f,{x,n}]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25571] Re: RE:[mg25495] ? D[f,{x,n}]
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Sun, 8 Oct 2000 00:41:58 -0400 (EDT)
  • References: <8rmlm3$2i9@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Ted
Re your observation:

> this
> seems to prove that D[f, {x, n}]  evaluates
>   Nest[ D[#, x]&, f, n ]
> or something equivalent.

The following supports this.

x /: x^3 = a[x];

D[x^5, {x, 3}]

20*Derivative[1][a][x]

Derivative[3][Function[x, x^5]]

Function[x, 20*Derivative[1][a][x]]

But,

f[x_] := x^5;

Derivative[3][f][x]

60*x^2


--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565






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