  In the paper we consider the problem of multivariate function approximation
in polynomial basis. In order to solve this problem, we adjust the least
squares method (LSM) by adding information about derivatives of the function.
This modification allows reducing the number of evaluations of approximating
function while keeping the accuracy at the appropriate level. We propose
several techniques for time-efficient calculation of derivatives in various
applications. Numerical examples are given for comparison between the standard
LSM and the proposed approach.
