Flash computation is the engine of any process simulation and its time-consuming takes typically 80~90% of simulation calculation. Flash derivatives with respect to feed inputs such as temperature, pressure, especially compositions are often the bottleneck to the speed-central simulations such as dynamic simulation, optimization and equation-based steady state simulation. In these calculations, a numerical implementation of those derivatives is very expensive and unstable, especially across phase boundary. In this work, we report explicit analytical derivatives in flash computation. These analytical results are developed based on Gibbs free energy minimization and its mathematical matrix transformation. Our derivatives have been validated by the conventional Rachford-Rice equation. Real calculation examples indicate that the analytical scheme is 30~40 times faster than the alternative numerical one and the time-saving increases with the increasing number of components in the flash stream. In addition, the computation is straightforward, avoiding any across phase boundary problems.