• Support PF! Buy your school textbooks, materials and every day products Here!

Derivative of an absolute value

  • #1
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
6,230
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
41,770
911
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.
 

Related Threads for: Derivative of an absolute value

  • Last Post
Replies
2
Views
8K
  • Last Post
Replies
5
Views
12K
  • Last Post
Replies
4
Views
5K
Replies
9
Views
2K
Replies
1
Views
10K
  • Last Post
Replies
2
Views
15K
Replies
12
Views
11K
Replies
4
Views
2K
Top