In various examples, a motion planner include an analytical function to predict motion plans for a machine based on predicted trajectories of actors in an environment, where the predictions are differentiable with respect to parameters of a neural network of a motion predictor used to predict the trajectories. The analytical function may be used to determine candidate trajectories for the machine based on a predicted trajectory, to compute cost values for the candidate trajectories, and to select a reference trajectory from the candidate trajectories. For differentiability, a term of the analytical function may correspond to the predicted trajectory. A motion controller may use the reference trajectory to predict a control sequence for the machine using an analytical function trained to generate predictions that are differentiable with respect to at least one parameter of the analytical function used to compute the cost values.