The neutron density is one of the most important dynamical parameters in a reactor. It is directly related to the control and stability of the reactor power. Any change in applied reactivity and some of dynamical parameters in the reactor causes a change in the neutron density. Lyapunov exponent method is a powerful tool for investigating the range of stability and the transient behavior of the reactor power. In contrast to the other linear stability methods, this method can be used for large perturbations and is not needed to construct Lyapunov function. In this work, the range of stability using Lyapunov exponent method is evaluated for neutron point kinetics equations with six-groups delayed neutrons. Here, effects of four set of applications, namely, step, ramp, sinusoidal, and temperature feedback reactivities on power reactor were investigated with Lyapunov exponent method. The results of qualitative analysis were compared with traditional methods and were in good agreement with other works.