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>
• 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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