Y= arcsin(x^2-1) Iit's Example 2 of chapter 6.6 inverse trigonometry functions in calculus 8th edition by James Stewart. I don't understand textbook...

Y= arcsin(x^2-1)

Iit's Example 2 of chapter 6.6 inverse trigonometry functions in calculus 8th edition by James Stewart.

I don't understand textbook explanation. Do I have to find its domain by restricting outer function by inner function?..

And What about domain of its derivative function??