Answer
$ 4x^{3}+6x^{2}+2x$
Work Step by Step
Use the product rule,
$\displaystyle \frac{d}{dx}[f(x)g(x)]=f^{\prime}(x)g(x)+f(x)g^{\prime}(x)$.
$f(x)=x^{2}+x^{3},\quad f^{\prime}(x)=2x+3x^{2}$
$g(x)=x+1,\quad g^{\prime}(x)=1$
$\displaystyle \frac{dy}{dx}=(2x+3x^{2})(x+1)+(x^{2}+x^{3})(1)$
$=2x^{2}+2x+3x^{3}+3x^{2}+x^{2}+x^{3}$
$=4x^{3}+6x^{2}+2x$
