the derivative is simple the change between the last 2 values
That would be true for a derivative with respect to time, if the difference in sample times for the two measurements is exactly 1 second (assuming standard units).
A derivative is the instantaneous rate of change as the interval approaches zero in the limit
Yes of course, but your comment is irrelevant for a digital computer and discrete data.
It can only be approximated computationally. Whether or not the average rate of change over 1 second is a good approximation depends on the how quickly the value is changing and on the user's accuracy requirements, neither of which have been specified.
It also fails to help correct the current misunderstanding in this thread.
But the red bold highlighting is a really, really nice touch!