Find the derivatives of the function

Question

k(x)=sqrt(sin(2x))^3

I think I have the answer and was wondering if i had it correct
k'(x)=2sin(x)^3+8sin(x)

Answer 1

I will interpret your question just the way you typed it

k(x) = √ [ (sin(2x) )^3 ] which is
= ( sin(2x) )^(3/2)

k ' (x) = (3/2)( sin(2x))^(1/2) ( cos(2x)) (2)
= 3 cos(2x) √(sin(2x))

Answer 2

ok thank you