# Derivative of an absolute value

1. Jun 8, 2008

### lLovePhysics

I don't get why: $$\frac{d}{dx}[|u|]=\frac{u}{|u|}(u')$$

Can someone give me an example to which this applies? Can you use any function in place of "u"?

2. Jun 8, 2008

### rock.freak667

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|

$$\frac{d}{dx}(|x|)=\frac{x}{|x|}$$

for x>0 ,|x|=x

and so $\frac{d}{dx}(x)=\frac{x}{x}=1$ which is true. Take x<0 and it'll also hold true.

3. Jun 9, 2008

### HallsofIvy

Staff Emeritus
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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