Derivatives, or Jacobians, are commonly required by numerical algorithms. Access to accurate Jacobians often improves the performance and robustness of algorithms, and in addition, efficient implementation of Jacobian computations can reduce the over-all execution time. In this paper, we present methods for computing Jacobians in the context of the Functional Mock-up Interface (FMI), and Modelica. Two prototype implementations, in JModelica.org and OpenModelica are presented and compared in industrial as well as synthetic benchmarks.