Derivative of an absolute value

  • #1
lLovePhysics
169
0
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"?
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,223
31
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.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
43,021
971
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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