Answer
The derivative is $4x^3-12x^2+6x-12$.
Work Step by Step
Product Rule: $g'(x)=((u(x)(v(x))’=u'(x)v(x)+u(x)v’(x))$
$u(x)=(x^2+3) ;u’(x)=(2x) $
$v(x)=(x^2-4x) ;v’(x)=(2x-4) $
$g'(x)=(2x)(x^2-4x)+(x^2+3)(2x-4)=$
$(2x^3-8x^2)+(2x^3+6x-4x^2-12)=$
$4x^3-12x^2+6x-12$
