((x+deltaX)^2+x+deltaX-(x^2+x))/deltaX = (x^2 + 2x delta x + (delta x)^2 + x + delta x - x^2 - x) / delta x = delta x (2x + delta x + 1) / delta x = 2x + delta x + 1
Therefore, Lim as x tends to 0 of ((x + delta X)^2 + x + deltaX - (x^2 + x)) / deltaX = 1 + delta x
