Not Understanding Derivative Notation

[Gibby_Canes]

In my Classical Mechanics book, one of the example problems makes a step that I do not understand. The steps are in the picture in the attachment. I do not understand how the left hand side goes from what it is in the first step to what it is in the second step. I have a poor understanding of Leibniz notation, so please keep that in mind in your responses.

 

[Muphrid]

This is just taking the product rule in reverse.

$$2 \dot x \ddot x = 2 v v' = (v v' + v' v) = (v^2)'$$

 

[Gibby_Canes]

Wow thanks. I do not know why that had me so stumped. I should probably sleep more.

Also, I just realized this probably should've been posted elsewhere. I was doing mechanics so I just went straight to the mechanics section. Apologies to anyone reading this.