Derivative of arcsin(cos(2x))
is this chain rule?

Yes, you need to use the chain rule. Also you need to use the derivative of arcsin which is in tables.

Derivative of y = arcsin(x) = 1 / [√(1 - x^2)]

Chain rule: Derivative of archsin(cos(2x)) =

y' = 1 / [√(1 - (cos(2x))^2)] *  derivative (cos(2x) =

y' = 1 / [√(1 - (cos(2x))^2)] * (- sin (2x)) * 2

y' = -2(sin(2x)) / [√( 1 - (cos(2x))^2]