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Re: Abs[x] function

• To: mathgroup at smc.vnet.net
• Subject: [mg87849] Re: Abs[x] function
• From: dh <dh at metrohm.ch>
• Date: Fri, 18 Apr 2008 07:11:11 -0400 (EDT)
• References: <fu9fn7$c8d$1@smc.vnet.net>

Hi Vlad,

by default Mathematica uses complex numbers. As Abs is not an analytical 

function, it does not have a derivative (the differential quotient 

depends on direction). Therefore, the derivative of Abs is not defined. 

For your application, you could define the derivative you would like to 

have yourself by e.g.:

Unprotect[Abs];

Abs'[x_]:=Which[x<0,-1,x==0,"undefined",x>0,1];

hope this helps, Daniel



Vladislav wrote:

> Who can explain the behavior. THe derivative Abs[x] at x=.5 is well

> defined and is equal to 1.

> 

> In[1]:= D[Abs[x], x]

> 

> Out[1]=

> \!\(\*SuperscriptBox["Abs", "\[Prime]",

> MultilineFunction->None]\)[x]

> 

> In[2]:= % /. x -> .5

> 

> Out[2]=

> \!\(\*SuperscriptBox["Abs", "\[Prime]",

> MultilineFunction->None]\)[0.5]

>