Answer
$2x(2x+3)(7x+2)+ 2x^{2}(7x+2)+ 7x^{2}(2x+3)$
Work Step by Step
Following example 1b, a more general product rule was introduced:
$(f\cdot g\cdot h)^{\prime}=f^{\prime}gh+fg^{\prime}h+fgh^{\prime}$
$f(x)=x^{2},\qquad f^{\prime}(x)=2x$
$g(x)=2x+3,\qquad g^{\prime}(x)=2$
$h(x)=7x+2,\qquad h^{\prime}(x)=7$
$\displaystyle \frac{dy}{dx}=(f\cdot g\cdot h)^{\prime}(x)=$
$=2x(2x+3)(7x+2)+ x^{2}(2)(7x+2)+ x^{2}(2x+3)(7)$
$=2x(2x+3)(7x+2)+ 2x^{2}(7x+2)+ 7x^{2}(2x+3)$
... we do not need to expand the answer..