This report is the result of a joint discussion between the Rubin and Euclid scientific communities. The work presented in this report was focused on designing and recommending an initial set of Derived Data products (DDPs) that could realize the science goals enabled by joint processing. All interested Rubin and Euclid data rights holders were invited to contribute via an online discussion forum and a series of virtual meetings. Strong interest in enhancing science with joint DDPs emerged from across a wide range of astrophysical domains: Solar System, the Galaxy, the Local Volume, from the nearby to the primaeval Universe, and cosmology.