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Re: Question about the derivative of Abs

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106144] Re: Question about the derivative of Abs
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.net>
  • Date: Sat, 2 Jan 2010 05:08:41 -0500 (EST)
  • References: <hhkj64$53d$1@smc.vnet.net>

Sam Takoy <samtakoy at yahoo.com> wrote:
> Hi,
>
> I kind of asked this question before, but in a more confusing context,
> so now I would like to ask it by itself.
>
> In the course of my computations, I get Abs' and Abs''. It is applied to
> a positive number, so I think those values should be 1 and 0. However,
> Mathematica fails to simplify it.
>
> For example
>
> In[34]:= Abs'[2.0]
>
> Out[34]=
> \!\(\*SuperscriptBox["Abs", "\[Prime]",
> MultilineFunction->None]\)[2.]
>
> These expressions really mess up my answers. How do I get Mathematica to
> do these simplifications?

I don't know why you're getting Abs' and Abs'' in your answers, but perhaps
it's just because you have asked for derivatives of expressions involving
Abs itself. If that is the case, then you might consider avoiding Abs in
your input by instead using Sqrt[x^2] when x is real.

In[1]:= D[Sqrt[x^2], x]

Out[1]= x/Sqrt[x^2]

In[2]:= D[%, x]

Out[2]= -(x^2/(x^2)^(3/2)) + 1/Sqrt[x^2]

In[3]:= Simplify[{%%, %}, x > 0]

Out[3]= {1, 0}

David


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