So I use chain rule, which also involved use of the quotient rule.
5[(3x^2 + 2x + 1) / (3 - 2x^3 + x^2)]^4 * [(3 - 2x^3 + x^2) (6x+2) - (3x^2 + 2x + 1) (-6x^2 + 2x)] / (3-2x^3 + x^2)^2
Am I on the right track? It seems awfully long and I suspect I messed something up.