We propose and experimentally demonstrate a microwave photonic intensity differentiator based on a Kerr optical comb generated by a compact integrated micro-ring resonator (MRR). The on-chip Kerr optical comb, containing a large number of comb lines, serves as a high-performance multi-wavelength source for implementing a transversal filter, which will greatly reduce the cost, size, and complexity of the system. Moreover, owing to the compactness of the integrated MRR, frequency spacings of up to 200-GHz can be achieved, enabling a potential operation bandwidth of over 100 GHz. By programming and shaping individual comb lines according to calculated tap weights, a reconfigurable intensity differentiator with variable differentiation orders can be realized. The operation principle is theoretically analyzed, and experimental demonstrations of the first-, second-, and third-order differentiation functions based on this principle are presented. The radio frequency amplitude and phase responses of multi-order intensity differentiations are characterized, and system demonstrations of real-time differentiations for a Gaussian input signal are also performed. The experimental results show good agreement with theory, confirming the effectiveness of our approach.