chain rule using trig functions So I have the following:
$$
y = cos(a^3 + x^3)
$$
This is what I got.
$$
y' = \cos(a^3 + x^3) \ ( -sin(a^3 + x^3) ) \ ( 3a^2 + 3x^2 )
$$
I'm not sure what to do after this? Would this be the final answer?

What you wrote is not correct.  Assuming $x$ is the variable, the correct answer is 
$y' = -\sin(a^2+x^3)3x^2$
