How to go from $x_{p}\frac{dx_{p}}{dt}$ to $\frac{d}{dt}(\frac{1}{2}x_{p}^{2})$?

Question

I have the following example:

Example that contains my problem

I cannot seem to find out how they go from $ x_{p}\frac{dx_{p}}{dt}$ to $\frac{d}{dt}(\frac{1}{2}x_{p}^{2})$.