Question

FIND DERIVATE (X^2-1)^3(x^2+2) USING PRODUCT

Answer 1

\[(f')(g)+(f)(g')\] where f is (x^2-1)^3 and g is (x^2+2) I think is what you're trying to say. Use this site to help you http://www.wolframalpha.com/

Answer 2

using product rule
d/dx (x^2-1)^3*(x^2+2)+(x^2-1)^3*d/dx (x^2+2)
using chain rule for (x^2-1)^3 (i.e. d/dx (x^2-1))
3(x^2-1)^2*d/dx(x^2-1)*(x^2+2) + 2x(x^2-1)^3
6x(x^2-1)^2(x^2+2)+2x(x^2-1)^3
factor out 2x(x^2-1)^2
2x(x^2-1)^2*(3(x^2+2)+(x^2-1))
2x(x^2-1)^2(3x^2+6+x^2-1)
2x(x^2-1)^2(4x^2+5)
and, I dont believe it matters which you choose for f and g as long as you keep it consistent throughout.