Use the product rule to differentiate y=x²(3x²+4)³

y'=18x^3(3x^2+4)^2+2x(3x^2+4)^3

u=x^2
v=(3x^2+4)^3

y'=u' v + v' u

The Product rule states:
D[f(x)g(x)] = f(x)Dg(x) + g(x)Df(x), so:

D[x^2 (3x^2+4)^3] =x^2 [3(3x^2+4)^2(6x)] + 2x(3x^2+4)^3

Combining like forms: 18x^3 (3x^2+4)^2+2x(3x^2+4)^3

y'[x] = 8 x (1 + 3 x^2) (4 + 3 x^2)^2