The problem: $x^3\sqrt{2x+4}$
$f(x):= x^3$, $g(x):= \sqrt{2x+4}$
(f\times g)' = f^{\prime}g+fg^{\prime} thus it should be
$3x^2\sqrt{2x+4} + (x^3)[\frac{1}{2}(2x+4)^{\frac{-1}{2}}(2)]$
which is $3x^2\sqrt{2x+4}+\frac{x^3}{\sqrt{2x+4}}$
The book gives: $3x^2\sqrt{2x+4}+\frac{x^3}{2\sqrt{2x+4}}$
I'm correct? I always get worry when my answers don't match the book.
$\frac{d}{dx}[f\times g(h(x))] = f^{\prime} \times g(h(x))+ f\times g^{\prime}(h(x))h^{\prime}$ right?