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Deep learning holds a great promise of revolutionizing healthcare and medicine. Unfortunately, various inference attack models demonstrated that deep learning puts sensitive patient information at risk. The high capacity of deep neural networks is the main reason behind the privacy loss. In particular, patient information in the training data can be unintentionally memorized by a deep network. Adversarial parties can extract that information given the ability to access or query the network. In this paper, we propose a novel privacy-preserving mechanism for training deep neural networks. Our approach adds decaying Gaussian noise to the gradients at every training iteration. This is in contrast to the mainstream approach adopted by Google's TensorFlow Privacy, which employs the same noise scale in each step of the whole training process. Compared to existing methods, our proposed approach provides an explicit closed-form mathematical expression to approximately estimate the privacy loss. It is easy to compute and can be useful when the users would like to decide proper training time, noise scale, and sampling ratio during the planning phase. We provide extensive experimental results using one real-world medical dataset (chest radiographs from the CheXpert dataset) to validate the effectiveness of the proposed approach. The proposed differential privacy based deep learning model achieves significantly higher classification accuracy over the existing methods with the same privacy budget.