Differentiation using product rule I'm having trouble simplifying these questions, particularly when they involve square roots of $x$.
Differentiate the following with respect to $x$ and simplify:
$y=(x+2)x^\frac{3}{2}$
My attempt:
Using product rule: $u=x^\frac{3}{2}, v=(x+2)$ therefore $\frac{du}{dx}=\frac{3}{2}x^\frac{1}{2}, \frac{dv}{dx}=1\\$
$\frac{dy}{dx}= \frac{3\sqrt{x}}{2}(x+2)+(\sqrt{x})^3$
Factorise:$\sqrt{x}[\frac{3}{2}(x+2)+(\sqrt{x})^2]\\\sqrt{x}[\frac{3}{2}x+3+x]$
The given answer is $\frac{\sqrt{x}}{2}(5x+6)$, which I can't achieve and I can't understand why the denominator of 2 is a common factor.

A general rule: first simplify, then differentiate.  The function in question is a product, namely $$y=(x+2)x^\frac{3}{2}.$$
 First simplify it to a sum
$$y=x^{\frac{5}{2}}+2x^\frac{3}{2}$$
and then  differentiate 
$$y’=\frac{5}{2}x^{\frac{3}{2}}+3x^{\frac12}.$$
