We introduce Differentiable Neural Radiosity, a novel method of representing the solution of the differential rendering equation using a neural network. Inspired by neural radiosity techniques, we minimize the norm of the residual of the differential rendering equation to directly optimize our network. The network is capable of outputting continuous, view-independent gradients of the radiance field with respect to scene parameters, taking into account differential global illumination effects while keeping memory and time complexity constant in path length. To solve inverse rendering problems, we use a pre-trained instance of our network that represents the differential radiance field with respect to a limited number of scene parameters. In our experiments, we leverage this to achieve faster and more accurate convergence compared to other techniques such as Automatic Differentiation, Radiative Backpropagation, and Path Replay Backpropagation.