I think integrating would be better, because it seems wrong to judge a products "success" only at some specific instant of time, rather than judging it over a full period of time.

The sign of the first derivative only gives you the present rate of adoption/abandonment of the platform, while integrating gives you a measure of success over the platform's entire existence.

I was just answering his question. Thank you for defining the opposing view quantitatively. I have never used a nokia phone, but certainly I would count myself a success if I had area under the curve like that.

At which point on the curve?

the window defined by his data points