Recently, we introduced a parallel-beam two-pass analytical reconstruction that allows truncation to be accounted for in the image domain rather than the projection domain. In particular, we showed that backprojection of a vastly angularly undersampled sinogram of un-truncated data could be used to extrapolate the backprojection of a finely sampled, fully truncated sinogram of the same object to perform more accurate region-of-interest (ROI) imaging. The same extrapolation idea can be performed using differentiated backprojection (DBP). The goal of this study is to give a general DBP-based formula when reconstructing a finite set of projections in parallel geometry. We discuss the discretization of this formula, in particular when the image grid size is large with respect to the number of projections, and we show how it can be applied to our extrapolation problem.