In the field of automatic speech recognition (ASR), it is common practice to augment features with time-derivatives, which we call derivative-augmented features (DAF). Although the method is effective for modeling the dynamic behavior of features and produces significantly lower classification error, it violates the assumption of conditional independence of the observations. The traditional approach is to ignore the problem (simply apply the mathematical approach that assumes independence). In this paper, we take an alternative approach in which we still use the same mathematical approach as before, but calculate a correction factor by integrating out the redundant dimensions. This makes it possible to compare and combine a DAF PDF and a non-DAF PDF. We conduct experiments to demonstrate the usefulness of the approach.