Re: Re: Forcing a Derivative

*To*: mathgroup at smc.vnet.net*Subject*: [mg50834] Re: [mg50819] Re: Forcing a Derivative*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Thu, 23 Sep 2004 05:27:15 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200409220412.AAA18753@smc.vnet.net>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

I see no difficulty in: f[x_] := x^2 + 7 f'[x] 2x + 7 f'[y] 2y + 7 even if one also has a definition for x[y_] or y[x_]. When f has one argument -- and at least so far that's all that's at issue here -- f' is the derivative of f, that is, stands for f'[#]&, so whatever the argument given in something of the form f'[expr], the result would be the value of the derivative at that input expr. x[y_] Bill Rowe wrote: > On 9/21/04 at 3:49 AM, murray at math.umass.edu (Murray Eisenberg) > wrote: > > >>So really the questions is: WHY doesn't -- or, perhaps, why >>shouldn't -- Mathematica understand such things as (f g)'? Or (f + >>g)' ,etc.??? > > > I think there are several issues here. First, how should Mathematica interpret f'? Sure, it is the derivative of f. But with respect to what? Yes, if I saw f was defined as x^2 + 7, I would assume f' meant df/dx. But is it reasonable for Mathematica to make this assumption when it is intended to be very general? > > Note > > f[x_] = x^2 + 7 > x^2 + 7 > > Head[f] > Symbol > > Head[x] > Symbol > > The point being x and f have the same head and are not clearly distinct. So, there could have been a previous definition such as x[y_] = 2 y. If this were the case, what should Mathematica do? Compute df/dx ignoring the definition for x or compute df/dy? > > > Also, realize the original poster did define f as I did above, that is something to operated on an expression. Consequently, f' is really undefined since no argument as been supplied. Contrast > > f[x] > x^2 + 7 > > with > > f[2*x] > 4*x^2 + 7 > > Again, this raises the question of what Mathematica should return for f'. It seems to me the only logical choice is to do what Mathematica currently does, return f' as unevaluated. > > Finally note had the original poster defined f as a pure function i.e., > > f = #^2+7& > > then f' and f'' return pure functions that are the expected derivatives, i.e., > > f' > 2*#1 & > > f'' > 2 & > > When f is defined as a pure function in this manner, Mathematica knows f has only one argument and the only reasonable interpretation of f' is the derivative of f with respect to that argument. This is quite different than writing f[x_]= and later not supplying the argument x. > -- > To reply via email subtract one hundred and four > > -- 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

**References**:**Re: Forcing a Derivative***From:*Bill Rowe <readnewsciv@earthlink.net>

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**Arg[z] that works with zero argument?**

**Re: Forcing a Derivative**

**Re: Forcing a Derivative**