Determine g(x+a)−g(x) for the following function. g(x)=−x2−x

Answer 1

g(x+a) = -(x+a)^2 - (x+a) = -x^2 -2ax -a^2 -x -a

g(x) = -x^2 - x

g(x+a) = -2ax -a^2 -a

usually the rest of the problem is divide by a to get -2x-1 -a

then take the limit as a approaches zero to get -2x-1-0 = -2x-1 which equals the derivative of g(x)