I have no idea how to do this problem I am suppose to find the derivative of $y=\cos(a^3 + x^3)$ but I do not really know how to start this problem. At first I thought I could use the sum rule and just make it $3a^2$ and $3x^2$ but for some reason I do not think that is correct, possibly because I am solving for $x$ and for some rule I can not get the derivative of a like that.
Anyways what I tried was using the product rule which gave me $\cos(a^3 + x^3)\prime -\sin(a^3 + x^3)$ not sure if that makes sense but I attempted to get the derivative of $(a^3 + x^3)$ using the chain rule and I got completely the wrong answer. I ended up with this abomination, $3\cos(a+x)^2 -\sin(a^3 + x^3)$