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]