# Not Understanding Derivative Notation

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.

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