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Approximation theory, Computational Mathematics and Numerical analysis in the context of Computational (numerical) diameter. From the ideological point of view  C(N)D-study consists of three parts – C(N)D - 1, -2, -3: C(N)D-1 (recovery by accurate information, depending on the type of functionals and algorithms for processing numerical information obtained from them, includes all known approximation theory, numerical analysis, computational mathematics, theory of functions – Fourier series, bases), C(N)D - 2 (in an optimal computational aggregate, the values of information functionals can be replaced with values close to them, the search for the largest such discrepancies forms an independent problem of finding limiting errors – a new optimization problem) and C(N)D - 3 (there exists or does not exist another computational aggregate with a structure similar to the structure of the considered optimal computational aggregate, and even, perhaps, more general, but with a larger limiting error in order). It is considered the concretization of C(N)D-study in the case of "Numerical differentiation of functions".