the -1/2 is to account for the -2 that was put in front of the x (noticed the -2x?). what they did was multiply the x by -2 and then divide by -2 (hence the -1/2) so as to not change anything. why? because -2x is the derivative of 4 - x^2. why do we care? well, in this set up, it is "easy" to see that we have an expression that is the result of using the chain rule to differentiate a function. basically what happened here is doing substitution without actually saying "let u = 4 - x^2." this is a more clever and concise way of doing it
EDIT: Beaten again...twice...and with better explanations too good job guys