Question

Find the derivative of____(below)
and indicate points at which f'(X) does not exist.

Answer 1

Umm I have an approach, maybe this is over-complicating it though..

Recall: \(\Large |x|\quad=\quad \sqrt{x^2}\)

So we can write our expression as:\[\Large f(x)\quad=\quad \sqrt{\left(\sqrt{x^2}-1\right)^2}\]
From there, we can take the derivative and apply the chain rule a couple times.

Answer 2

oh ok, got it thanks!!

Answer 3

Oh figured it out already? XD

Answer 4

yeah,wait a sec. let me double check my answer,

Answer 5

That approach seems fine.
Maybe this makes more sense though.
Note that:\[\Large \left(|x|\right)' \quad=\quad \frac{x}{|x|}\](You could use the sqrt thing to show this fairly easily).
Which will lead us to this:\[\Large \left(\left||x|-1\right|\right)' \quad=\quad \frac{|x|-1}{\left||x|-1\right|}(|x|-1)'\]

Answer 6

Bah! So many absolute lines lol.

Answer 7

\[\Large \left(\left||x|-1\right|\right)' \quad=\quad \frac{|x|-1}{\left||x|-1\right|}\left(\frac{x}{|x|}\right)\]

Answer 8

I'm confused the correct answer is:
I did wrong..
can you show/explain me how to get this answer??
btw, it's not a homework, i'm just practicing and I found this question somewhere in my book.