2) The unit vector is the vector given divided by its magnitude. That is how it is defined. So to find the unit vector you find the magnitude of the given vector, in this case 5 and then divide each component in the vector by it.
For this you use the derivative over a function rule. The top of the fraction is x, the derivative of the bottom is 2x.
So pull out of a half (or you could say multiply the top by 2 and bring out a half in front) to get (1/2) X 2x/(x^2+3).