This paper presents a novel approach to the Discrete Choice Model (DCM), which is essential for modeling human decision-making processes, called the Differentiable Discrete Choice Model (Diff-DCM). While conventional DCMs heavily rely on domain knowledge from experts, Diff-DCM can automatically learn, predict, and control interpretable models based on data through differential programming. It estimates an interpretable closed-form utility function that reproduces observed behaviors with only input features and choice outcomes without prior knowledge, and experiments on synthetic and real data show that it is applicable to various types of data and can be estimated quickly with a small amount of computational resources. In addition, it shows that differentiability can be utilized to provide insights such as optimal intervention paths for effective behavior change.