The first derivative of a curve is obtained by a simple mathematical operation and describes the slope of that curve at a given point. The steeper the slope of a curve at a given point, the higher the first derivative at this point. Consequently, a sigmoidal transition results in a peak-shape in the first derivative. The maximum of the peak is identical to the inflection point of the original curve. The broadness of the first derivative peak describes the temperature range the transition spans.

In general, sharp peaks in the first derivative and correspondingly sharp transitions in the original curve reflect a high thermodynamic stability. In addition, sharp transitions with a very steep slope also result in high amplitudes of the first derivative peak, again an indication for high thermodynamic stability.