First of all, remember that a square root is a power of $\displaystyle \frac{1}{2}$.
You have a product of functions, so use the product rule.
$\displaystyle \frac{dy}{dx} = (2x+1)^{\frac{1}{2}}\times \frac{d}{dx} (x^3) + x^3 \times \frac{d}{dx}[(2x+1)^{\frac{1}{2}}]$.
To work out the second of the derivatives, use the chain rule.