Approximation and reconstruction of the derivatives of functions satisfying mixed Hölder conditions

We obtain upper and lower bounds for the best accuracy of approximation in Stechkin's problem for the differentiation operator and in the problem of the reconstruction of the derivative from the values of the function at a given number of points for Nikol'skii and Besov classes of functions satisfying mixed Hölder's conditions. These estimates give the order of these quantities for almost all values of the parameters involved.