We focus on the difference between differentiable versus strict differentiable locally Lipschitz functions from the view point of nonsmooth analysis: while in the latter class, all limiting Jacobians are singletons, we show that there exists a differentiable locally Lipschitz function whose limiting Jacobian represents all nonempty compact connected subsets of matrices. In the particular case of real-valued functions, we obtain differentiable functions with surjective limiting and Clarke subdifferentias. In this case, our concrete example-scheme will also reveal that the class of such pathological locally Lipschitz differentiable functions is dense (for the topology of the uniform convergence) and spaceable (for the Lip-norm topology). The talk is based on the works: A. Daniilidis, R. Deville, S. Tapia-Garcia: All convex bodies are in the subdifferential of some everywhere differentiable locally Lipschitz function, Proc. London Math. Society (3) 129 (2024), no. 5, Paper No. e70007, 27 pp., DOI http://dx.doi.org/10.1112/plms.70007 A. Daniilidis, S. Tapia-Garcia: Differentiable functions with surjective Clarke Jacobians hal-04952836 (Preprint 15p, 2025)