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

**Follow-Ups**:**Re: Re: Re: Forcing a Derivative***From:*DrBob <drbob@bigfoot.com>

**References**:**Forcing a Derivative***From:*"Scott Guthery" <sguthery@mobile-mind.com>

**Re: Forcing a Derivative***From:*Andrzej Kozlowski <andrzej@akikoz.net>