Derivative
If f is a real function, and h is infinitesimal, and if f ′(x) exists, then the derivative is defined as
Explanation
Alternatively, if y = f ′(x), one takes an infinitesimal increment Δx, and computes the corresponding Δy = f (x + Δx) − f (x). One forms the ratio . The derivative is then defined as the standard part of the ratio:
Examples
If you drive 30 km on a bicycle in 2 hours, you can calculate the speed as 30 / 2 = 15 km/h.
If you suddenly put the breaks in a car that has a speed of 80 km/h, and you stand still within 10 seconds, you can derive the braking force. Because 80 km/h / 10 sec = 2,2 m/sec2.