# Math Help - derivation of absolute value

1. ## derivation of absolute value

Hi everyone

I've a question involving derivation of absolute values, if you look at the attached picture you will see what I couldn't understand as shown in a rectangle. I couldn't get that part. It will be much appreciated if someone can explain how it happens

thanks...

2. $y = \sqrt{u^2}$

We use the chain rule to differentiate this. Differentiate the square root, then the inside part:

$(\sqrt{u^2})' = \frac{1}{2\sqrt{u^2}} \cdot 2u$

$= \frac{\not{2}u}{\not{2}\sqrt{u^2}}$

$= \frac{u}{\sqrt{u^2}}$

$= \frac{u}{|u|}$

You have to know that, if n is even, then:
$\sqrt[n]{x^n} = |x|$

3. got it many thanks...