The correlated derivative propagation method is proposed for the time evolution of quantum wave packets. Without truncation of higher derivatives of hydrodynamic fields, the exact equations of motion derived in the derivative propagation method are solved through the Taylor series method by propagating correlated quantum trajectories. By mapping the physical grid to a uniform computational grid, the necessary higher derivatives of these fields are computed by the finite difference method, and the Jacobian terms of the transformation are determined by the moving least squares method. The Taylor coefficients for hydrodynamic fields and their derivatives are evaluated exactly using the automatic differentiation technique. Excellent results are obtained for barrier transmission problems. Published by Elsevier B.V.