Answer
$$ y''=20x^3+12x^2+2, \quad y'''=60x^2+24x.$$
Work Step by Step
Let $ y=(x^2+x)(x^3+1)$; first we simplify $ y $ as follows
$$ y=(x^2+x)(x^3+1)=x^5+x^4+x^2+x.$$
Now, we get
$$ y'=5x^4+4x^3+2x+1$$
$$ y''=20x^3+12x^2+2, \quad y'''=60x^2+24x.$$
