Dot product step in deriving the Liouville equation

[oristo42]

So, while textbook was deriving Liouville eq, this is one of step the book uses. I don't understand this step at all. Why is this step true?

 

[jedishrfu]

I think its the product rule for the del operator:

The power of the del notation is shown by the following product rule:

https://en.wikipedia.org/wiki/Del