Partial derivative evaluating formulae from a data given on the nodes of a regular planar grid

This study focuses on the evaluation of partial derivatives of a bivariate function with respect to its arguments from the function's known values at the nodes of a rectangular (;rid. Although evaluation is based on the truncated Taylor series expansion of the function at a midpoint in its analyticity domain, it can also be related to Lagrange polynomials despite we do not focus on this direction here. We use direct products of the vectors (and matrices). This is due to cartesian product nature of the data domain. Direct product utilization reduces computational complexity since it somehow enables us to deal with each dimension independently. What we have developed and revealed here can be applied to the multivariances beyond the bivariate case without any remarkable difficulty.