1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper

    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|


    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


    User Avatar
    Science Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook