Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 122: 32

$$ h'(s) =(s+4)(s^2+1)+s(s^2+1)+2s^2(s+4).$$

Since $ h(s)=s(s+4)(s^2+1)$, then the derivative, using the product rule, is given by $$ h'(s)=s'(s+4)(s^2+1)+s(s+4)'(s^2+1)+s(s+4)(s^2+1)'\\ =(s+4)(s^2+1)+s(s^2+1)+2s^2(s+4).$$