Find dy/dx if y= x^6[(x^2-9)^8]?

Question

So the answer is supposed to be 2x^5[(x^2-9)^7](11x^2-27), but I don't understand how to get it. Do you use product rule, chain rule or both?

thanks

Answer 1

Actually I figured out that you use both, and ended up with 16x^7(x^2-9)^7 + 6x^5(x^2-9)^8.

but I don't understand how that simplifies to 2x^5(x^2-9)^7(11x^2-27)?

Answer 2

factor out 2x^5(x^2-9)^7 and you have
2x^5(x^2-9)^7 * (8x^2 + 3(x^2-9))
= 2x^5(x^2-9)^7 (8x^2+3x^2-27)
and voila...