English: Graph of the characteristic curve of an electrical device with negative differential resistance (red portion of curve), showing how negative differential resistance is defined. The differential resistance r_diff at a point P on the curve is equal to the inverse slope of the curve at that point

${\displaystyle r_{\text{diff}}(P)={dv \over di}(P)\,}$

This is equal to the slope of the line tangent to the graph at that point

${\displaystyle r_{\text{diff}}(P)={\frac {\Delta v}{\Delta i}}={\frac {v_{2}-v_{1}}{i_{2}-i_{1}}}\,}$

Since   ${\displaystyle \Delta v>0\,}$   and   ${\displaystyle \Delta i<0\,}$,   therefore   ${\displaystyle r_{\text{diff}}<0\,}$   the differential resistance is negative at point P.