For the first 1.
Differentiating wrt :
Since ,
Why would you simplify? There are a few reasons. Mainly if you are using it in some future equation though. It makes it much much easier to write, so if you are actually using the result in a larger equation it makes it easier to keep track of things.
Secondly, while it doesn't matter in your case, consider the derivative of . YOu can of course rewrite it in it's current form to be and use something like the product rule or the chain rule to solve, which would be long and complicated. Or you could note that is just 1, hence the derivative is zero. and so on and so forth.
It is a good habit to get into to simplify as much as possible before doing the work. As Skeeter says, work smart not hard, which is something that applied mathematicians (like me) believe in. I once had a lecturer who found out that the place that we had our class was the other side of campus (maybe a ten minute walk) and was too lazy to walk out that far (possibly had other classes to be fair), so he moved the room, and we spent the entire semester squashed up in a room that was waaay to small to hold the entire class. Be lazy about things.