A changing rectangle gains area along both edges.
The exact change is (f+Δf)(g+Δg)−fg=gΔf+fΔg+ΔfΔg. Divide by h and let h approach zero. For differentiable f,g, the corner term divided by h tends to zero, leaving f′g+fg′. Here f=x+1 and g=x².
The finite corner is real, but it disappears after division by h and passage to the derivative limit.