The concept of partial derivatives of numbers is considered to study the stability of solutions of systems of differential equations. The conditions and criteria for the use of partial and external derived numbers are proposed. This makes it possible to investigate the behavior of a function of several variables, without requiring its differentiability, but using only information about partial derivative numbers. This reduces the restrictions on the degree of smoothness of the functions being studied. The proposed method can be used to obtain the necessary or sufficient conditions for the stability of solutions of systems of differential equations.