y = [arcsin√(x - 1)]²
y' = 2•arcsin√(x - 1) • [arcsin√(x - 1)]'
= 2arcsin√(x - 1) • 1/√{1 - [√(x - 1)]²} • [√(x - 1)]'
= 2arcsin√(x - 1) • 1/√(2 - x) • 1/[2√(x - 1)] • (x - 1)'
= 2arcsin√(x - 1) • 1/√(2 - x) • 1/[2√(x - 1)] • 1
= [arcsin√(x - 1)]/√[(2 - x)(x - 1)]