Pretty sure I got this right, my online math homework program says it's wrong though

Find the derivative of the function

$\displaystyle y=(x^2+2)(\sqrt[3]{x^2+3})$

After working through it using chain rule and product rule, I found

$\displaystyle \frac{8x^3+22x}{3(x^2+3)^\frac{2}{3}}$

What did I do wrong?

Thanks!