How do you differentiate g(y) =(x^2 + 3)(x^3 + 4)  using the product rule?

$g ' \left(x\right) = 2 x \left({x}^{3} + 4\right) + \left({x}^{2} + 3\right) \cdot 3 {x}^{2}$
$\left(u v\right) ' = u ' v + u v '$
$g ' \left(x\right) = 2 x \left({x}^{3} + 4\right) + \left({x}^{2} + 3\right) \cdot 3 {x}^{2}$