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]
> >