Re: Abs function

*To*: mathgroup at smc.vnet.net*Subject*: [mg47318] Re: Abs function*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Mon, 5 Apr 2004 05:22:56 -0400 (EDT)*References*: <c4ge4p$5a$1@smc.vnet.net> <c4j8td$d00$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Jens-Peer Kuska <kuska at informatik.uni-leipzig.de> wrote: > tha mean that the derivative of Abs[] can be different for > real and complex arguments. For real arguments you have > > D[Abs[x], x] // FullSimplify[#, Element[x, Reals]] & > > Sign[x] It's interesting that that works as desired, considering that In[1]:= Assuming[Element[x, Reals], Simplify[D[Abs[x], x] ]] Out[1]= Abs'[x] doesn't work as desired. Anyway, perhaps my prior suggestion of rewriting in terms of UnitStep is still of some use since In[2]:= Integrate[Abs[x], x] // FullSimplify[#, Element[x, Reals]] & Out[2]= Integrate[Abs[x], x] doesn't work as desired. BTW, I didn't mention it in my prior post, but perhaps the nicest form for that real antiderivative is just 1/2*x*Abs[x]. Could anyone manage (without going to lots of trouble) to get Mathematica to give that form? Regards, David Cantrell > nikmatz wrote: > > i try to find the derivative of abs function > > > > D[Abs[x],x] > > > > and Mathematica answer > > Abs`[x] > > > > what mean that

**Follow-Ups**:**Re: Re: Abs function***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>