Ejemplo

Hallar la derivada de y = x^2 + 3x + 5.

1. Incrementar las variables:                                                                                                                                                 y + dy = (x + dx)^2 + 3(x + dx) + 5 = x^2 + 2x(dx) + dx^2 + 3x + 3dx + 5
2. Reducción de terminos:                                                                                                                          dy = (2x + 3) dx + dx^2
3. Aplicar la formula:                                                                                                                                   dy / dx = ((2x + 3) dx + dx^2) / dx = 2x + 3 + dx
4. Sacar el límite:    lím=0                                                                                                                                                  dy / dx = lim (2x + 3 + dx) = 2x + 3