Multifunctional photonic differentiation is robust in optical computing and optical signal processing. We theoretically propose a multifunctional optical differentiator based on phase modulation and linear filtering. We also experimentally demonstrate two kinds of differentiators by using a phase modulator cascaded a fiber delay interferometer (DI) whose transmission spectrum is approximately linear. Difference between the two differentiators relies on whether the differentiated signals are formed by the optical intensity or the optical field of the output signal, which in turn depends on the relative shift between the signal wavelength and the closest notches of a linear filter. We also show the average errors of all kinds of differentiations and results show that the increase of the degree of linearity of the transmission spectrum of the DI will reduce the average error. Moreover, we demonstrate multi-channel multifunctional differentiation due to the comb spectrum of the DI.