Answer
$y'=5x^4-12x^3+6x^2+2x-3$
$ y'(2)=9$.
Work Step by Step
Product Rule $y'=((u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$
$u(x)=(x^2-3x+2) ;u’(x)=(2x-3) $
$v(x)=(x^3+1) ;v’(x)=(3x^2) $
$y'=(2x-3)(x^3+1)+(x^2-3x+2)(3x^2)$
$=(2x^4+2x-3x^3-3)+(3x^4-9x^3+6x^2)$
$=5x^4-12x^3+6x^2+2x-3$
$y'(2)=5(2)^4-12(2)^3+6(2)^2+2(2)-3=9$
