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?

$$d[\cos(a^3+x^3)]=-\sin(a^3+x^3)d(a^3+x^3)=-\sin(a^3+x^3)3x^2dx$$
assuming $a$ is a constant and $x$ is the variable.  If you want to explicitly use the chain rule then let
$$u=a^3+x^3,\frac{du}{dx}=3x^2$$
$$y=\cos u,\frac{dy}{du}=-\sin u$$
$$\frac{dy}{dx}=\frac{du}{dx}\times\frac{dy}{du}=-3x^2\sin(a^3+x^3)$$
