sin(3x^4-2)^3 can mean
and if that's what you mean then your working is good except for a missing 'sin' between the (3) and the subsequent (3x^4-2). Edit: sorry, no you need to remove the power 3 from the cos, as well. In that case I'll do a pic, as well.
If sin(3x^4-2)^3 means
then that's another matter. [Oh... you did mean that, and it's all good.]