Differenciate cos[2sin^2(x^3)]

Answer 1

use the chain rule
y = cos cos[2sin^2(x^3)]
y' = -sin cos[2sin^2(x^3)] * (2 sin^2(x^3))'
= -sin cos[2sin^2(x^3)] * 2*2sin(x^3) * cos(x^3) * 3x^2

Answer 2

oops. sorry about that extra cos -- dang copy/paste ...
y = cos[2sin^2(x^3)]
y' = -sin[2sin^2(x^3)] * (2 sin^2(x^3))'
= -sin[2sin^2(x^3)] * 2*2sin(x^3) * cos(x^3) * 3x^2