Linear phase maximally flat digital differentiators (DDs) with stopbands obtained by minimizing the L_p norm are filters with important practical applications, as they can differentiate input signals without distortion. Stopbands designed by minimizing the L_p norm can be used to control the relationship between the steepness in the transition band and the ripple scale. However, linear phase DDs are unsuitable for real-time processing because each group delay is half of the filter order. In this paper, we proposed a design method for a low-delay maximally flat low-pass/band-pass FIR DDs with stopbands obtained by minimizing the L_p norm. The proposed DDs have low-delay characteristics that approximate the linear phase characteristics only in the passband. The proposed transfer function is composed of two functions, one with flat characteristics in the passband and one that ensures the transfer function has L_p approximated characteristics in the stopband. In the optimization of the latter function, Newton's method is employed.