The efficient computation of the DSST short period motion Fourier coefficients is important for Orekit DSST orbit determination applications, especially high accuracy applications where many of these coefficients are required. Currently these coefficients are computed with Lagrange interpolators because the time derivatives of the coefficients are not available. If both the coefficients and their time derivatives were available, we could employ Hermite interpolators. Such Hermite interpolators have proved advantageous for the DSST mean element equations of motion. But Orekit has implemented an automatic differentiation scheme for derivatives of complex software-defined functions. This issue requests implementation of the capability to compute the time derivatives of the DSST short period motion Fourier coefficients via automatic differentiation.