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Derivative of an absolute value

  1. Jun 8, 2008 #1
    I don't get why: [tex] \frac{d}{dx}[|u|]=\frac{u}{|u|}(u') [/tex]

    Can someone give me an example to which this applies? Can you use any function in place of "u"?
     
  2. jcsd
  3. Jun 8, 2008 #2

    rock.freak667

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    but you'd need to know that that isn't differentiable at u=0

    and for u>0 ,|u|=u
    and for u<0,|u|=-u

    for example take |x|

    [tex]\frac{d}{dx}(|x|)=\frac{x}{|x|}[/tex]


    for x>0 ,|x|=x

    and so [itex]\frac{d}{dx}(x)=\frac{x}{x}=1[/itex] which is true. Take x<0 and it'll also hold true.
     
  4. Jun 9, 2008 #3

    HallsofIvy

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    You can use any differentiable function in place of u.

    Do what you always do with an absolute value: consider cases u(x)>0 and u(x)< 0 separately.
     
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