Question

y=(arcsin√(x-1) )^2,求y的导数

Answer 1

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)]