  The multiferroics are the materials, where single cell of a magnetically
order crystal forms an electric dipole moment. We derive equation for the
evolution of the macroscopic density of the electric dipole moment
(polarization of the system). The derivation is made within the "quantum
hydrodynamic" method, which allows to derive equations for the evolution of the
macroscopic functions of the quantum systems starting with the microscopic
description. In this work we do not consider the microscopic level of
individual electrons and ions, but we start our analysis from the combination
of ions in cells of the crystal. We present an effective Hamiltonian for the
evolution of such intermediate scale objects. We also apply the equation for
the electric dipole moment of the single cell, which is recontracted in the
corresponding operator. Using this operator and the wave function of
combination of ions in the cell, we define the macroscopic density of the
electric dipole moment. Finally, we apply the nonstationary Schrodinger
equation with the chosen Hamiltonian in order to derive equation evolution of
the polarization. The derivation is made for the dipole formed by the
exchange-striction mechanism in the II-type multiferroic materials. The
interaction caused term in the polarization evolution equation is found to be
proportional to the fourth space derivative of mixed product (triple scalar
product) of three spin density vectors. Conditions are discussed for the
regime, where interaction appears in a smaller order on the space derivatives.
