An analytically extended function (AEFD) for modelling of lightning currents first derivatives is presented in this paper. Among other mathematical functions, Heidler's function is often used for approximating lightning currents of the first positive, first and subsequent negative strokes as given in the IEC 62305 Standard. Analytically extended function (AEF) may be used for these currents representation also, with the calculated parameters, but its second order derivative is not continuous as for Heidler's function. However, the current's first derivative may be approximated using AEFD, so that the second order current derivative is analytically obtained as the first derivative of AEFD, and thus the problem is circumvented. Least squares method is used for obtaining parameters of AEFD.