Reachability analysis for dynamical systems typically relies on the system’s Jacobian to bound sensitivity of solutions. This method fails for nonsmooth dynamical systems as the Jacobian becomes undefined at the points where the vector field is non-differentiable. Such models can be hybridized by gluing together several smooth subsystems or modes via transitions, but the accuracy of reachability degrades when reachable sets are propagated across the mode boundaries. We propose an alternative approach based on lexicographic differentiation. Lexicographic differentiation was introduced by Nesterov as a foundation for calculus for nonsmooth functions. Our algorithm computes linear bounds on sets of lexicographic Jacobians, which give bounds on trajectory sensitivities. This avoids hybridization, eliminates mode transition computations, and yields more accurate reachsets. On nonsmooth models, our method improves accuracy on average by 50%, compared to hybrid algorithms. It is also one of the first methods to effectively handle reachability of ReLU neural ODEs.