Modulus Differentiation

[kenhung123]

Can someone tell me how to correctly differentiate modulus functions?

I am quite unsure how to deal with modulus functions in the form of |f(x)| and f(|x|)

[brightsky]

Hmm..probably differentiate it on a case by case basis:

Like

You can write it as:

if

if

And so for and for

-------
Or I suppose you can write it as and solve from there if that makes any difference. :p

[kenhung123]

Hmm so its normal differentiation with a domain?

[stonecold]

Yeah, it is really important that you can rewrite a modulus function as a hybrid function, using restrictions on the domain.  You also have to be aware of cusps for which there is no gradient.

[kenhung123]

Alrighty, thanks guys

[kenhung123]

Hahaha