Question

What is the derivative of an absolute value?

Answer 1

`d/dx|\u|=u/|\u|*(du)/dx`

Explanation:

absolute value function like `y=|\x-2|`
can be written like this: `y=sqrt((x-2)^2)`

apply differentiation :

`y'=(2(x-2))/(2sqrt((x-2)^2))` `rarr`power rule

simplify,
`y'=(x-2)/|\x-2|` `where` `x!=2`

so in general `d/dxu=u/|\u|*(du)/dx`

I will put this on double check just to be sure.