$\frac{1}{\rho*c^2}*P*\frac{\partial P}{\partial t} = \frac{1}{\rho*c^2} *\frac{P^2}{2}*\frac{\partial}{\partial t} $
My professor did this derivative in class and I didn't quite understand it. I understand that the rho and c are held constant as well as nothing is differentiated with respect to time. However, I don't understand where the $1/2$ and $P^2$ come from.
Anything would help! Thanks.