y=x^2(arcsinx)^3

Answer 1

Product rule: (u•v)' = u'v + uv'

u = x²

u' = 2x

v = (arcsin(x))³

v' = 3(arcsin(x))²(1/√(1 - x²)

So y' = (2x)((arcsin(x))³ + (x²)[3(arcsin(x))²(1/√(1 - x²)]

I'll let you simplify as much as you want.

Answer 2

Product rule. Within product rule, do chain rule.

note: arcsin derivative is 1/sqrt(1-x^2)