The Attempt at a Solution
The first one is easy, just use the fact that δi = δ/δxi and it reduces to the sum from with i=1,2,3 of δxi/δxi = 1 + 1 + 1
I tried to do a similar thing with the second one, also using the fact that r = |x| = √(x dot x), but for some reason I can't make any progress. Since r is a scalar, can't I pull it out of the original dot product and have the following:
1/r * (∇ dot u)
Well, obviously I can't because that would give me 3/r rather than 2/r.
I've made no progress on the third one so far, so any advice is appreciated.