Abstract: To promote the main results of function approximation theory to the multivariate function, the following work was presented in this paper by some skills of combination formula:the unified expression of the high order difference quotient formulas of multivariate function was established; the difference formula of the high order directional derivative was proven; the approximate high order partial derivative was studied; and the second-order partial derivative of the multivariate function and the truncation errors of the center difference quotient of the Hessian matrix were given.