I am confused with this equation derivation

[rickp]

Hello, please take a look at the image below:
http://tinyurl.com/cnz2sut

I am confused as to how that square root transformed into 3/2 power... Isn't it suppose to be 1/2 power if it's a square root?

Thanks

 

[Studiot]

The term on the right with the 3/2 power is the result of the differentiation stated by the term on the left.

 

[rickp]

Ahh of course >.< I can't believe I didn't see that. I thought the variables could become a part of the differential d/dt without differentiating the entire equation... My mathematical mistake! lol