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MathGroup Archive 2004

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Re: Re: Forcing a Derivative

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50792] Re: [mg50765] Re: [mg50753] Forcing a Derivative
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Tue, 21 Sep 2004 03:49:15 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200409190756.DAA17973@smc.vnet.net> <200409200139.VAA27487@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

So really the questions is:  WHY doesn't -- or, perhaps, why shouldn't 
-- Mathematica understand such things as (f g)'?  Or (f + g)' ,etc.???

Is there something in the language design that would prevent a meaning 
(the conventional one!) being assigned?  Or is it just that this hasn't 
been implemented.

I note that I have persistently found this a frustrating limitation of 
the language when I have used it for teaching.  One of the more 
difficult things to teach is the concept of a function as itself an 
object that can be manipulated.  It would be awfully nice if Mathematica 
allowed that to be so.

Andrzej Kozlowski wrote:
 >
 > Mathematica does not understand that you mean by f*g the function that
 > takes x to f(x)*g(x). There are various ways to deal with this > issue...
 > On 19 Sep 2004, at 16:56, Scott Guthery wrote:
 >
 >>How does one force Derivative[n] to actually take the derivative?
 >>
 >>For example if ...
 >>f[x_] = x^2 + 7
 >>g[x_]=3x^3 + 23
 >>then
 >>Derivative[2][f * g]
 >>just puts a couple of primes on the product rather than actually
 >>computing the dervative.

Andrzej Kozlowski wrote:

> On 19 Sep 2004, at 16:56, Scott Guthery wrote:
> 
> 
>>*This message was transferred with a trial version of CommuniGate(tm) 
>>Pro*
>>How does one force Derivative[n] to actually take the derivative?
>>
>>For example if ...
>>
>>f[x_] = x^2 + 7
>>
>>g[x_]=3x^3 + 23
>>
>>then
>>
>>Derivative[2][f * g]
>>
>>just puts a couple of primes on the product rather than actually 
>>computing the dervative.
>>
>>Thanks for any insight.
>>
>>Cheers, Scott
>>
>>
> 
> Mathematica does not understand that you mean by f*g the function that 
> takes x to f(x)*g(x). There are various ways to deal with this issue, 
> but the simplest are:
> 
> Derivative[2][f[#]*g[#] &][x] // Expand
> 
> 60*x^3 + 126*x + 46
> 
> or
> 
> 
> Expand[D[f[x]*g[x], {x, 2}]]
> 
> 60*x^3 + 126*x + 46
> 
> 
> 
> Andrzej Kozlowski
> Chiba, Japan
> http://www.akikoz.net/~andrzej/
> http://www.mimuw.edu.pl/~akoz/
> 
> 

-- 
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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