       Re: Re: differentiation operator

• To: mathgroup at smc.vnet.net
• Subject: [mg100719] Re: [mg100662] Re: differentiation operator
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Thu, 11 Jun 2009 21:43:06 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <h0nulh\$be1\$1@smc.vnet.net> <200906102110.RAA00562@smc.vnet.net>
• Reply-to: murray at math.umass.edu

That works reasonable well. For example, all the following forms work OK
(in the last form I simulate the Mathematica 2D standard form):

d/dx Sin[x]
(d/dx) Sin[x]
(d Sin[x])/dx
d
-- Sin[x]
dx

However, what does NOT work as one might hope is...

d Sin[x]/x

...even though that is a perfectly acceptable, traditional (with a small
"t") mathematical form for the same derivative.

Of course the use of the d/dx ties everything to a particular variable.
Change from x to y or t or something else, and it's dead.

dh wrote:
> Hi Chee,
>
> I did not thoroughly test it, but if you define:
>
> \$Pre = # /. Times[ d expr_  Power[dx, -1]] :> D[expr, x] &
>
> the following examples work:
>
> d/dx x^2 -> 2x
>
> d/dx Sin[x] -> Cos[x]
>
> d/dx (x-x^3) -> 1-3x^2
>
> e.t.c
>
> Daniel
>
>
>
> Chee Lim Cheung wrote:
>
>> Hi All
>
>
>> My students have asked me whether it is possible to define the operator
>
>> df[x]/dx for differentiation rather than D[f[x],x]. The operator is
>
>> available in a palette but it does not seem to do anything other than for
>
>> display only.
>
>
>> Example: d/dx(x^2)=2x rather than D[x^2,x]=2x.
>
>
>> Am I missing something?
>
>
>> Thanks
>
>> Mr. Chee
>
>
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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