This paper investigates fixed-time nonsingular terminal sliding mode control of second-order nonlinear systems in the presence of matched and mismatched disturbances. Using estimation of the mismatched disturbance estimated by a fixed-time disturbance observer, a novel nonlinear dynamic sliding surface is designed. This estimation is utilized in designing a completely novel nonlinear dynamics sliding surface whereby the fixed-time convergence of the sliding motion is guaranteed in spite of mismatched disturbance. The convergence time of the closed-loop system including disturbance observer and control system is guaranteed to be uniform with respect to initial conditions. Moreover, the proposed controller avoids chattering phenomenon by producing a continuous control signal.