Consequently another important local response function has also become available directly from the density function: the Fukui function f(r)= s(r)/S. The step towards the search for higher response functions has been made by the analytical calculation of the derivatives [𝜕𝑓(𝐫) 𝜕𝑁] ⁄ 𝑣 and [𝜕𝑠(𝐫) 𝜕𝑁] ⁄ 𝑣 for the hydrogenic orbitals. This present work delivers a theoretical and computational scheme to obtain the local hypersoftness of atoms and their ions. This is possibly non-negligible reactivity index that contribute to the global changes of the state functions (ΔN, ΔE, Δ), formally replacing the nonlocal response functions, as demonstrated in our previous paper. Numerical tests of this concept present a collection of results for atoms and ions, and they are aimed at estimation of the role of first and second local derivatives of their density over N for the physically observable effects of change ΔN, ΔE, Δ induced in chemical reactions.