This paper investigates  double sampling series derivatives for bivariate functions defined on $\mathbb{R}^{2}$ that are in the Bernstein space.
For this sampling series, we  estimate some of the  pointwise and uniform bounds when the function satisfies some decay conditions.   The truncated series of this  formula allow us to approximate any order of partial derivatives for function   from  Bernstein  space   using only a finite number of samples from the function itself.
This sampling  formula will be useful  in the approximation theory and its applications, especially after having the truncation  error    well-established.  Examples with tables and figures are given at the end of the paper  to illustrate the advantages of this formula.

关键词： double sampling series ,  truncation error bounds ,   convergence rate