Dermatological diagnosis automation is essential in addressing the high prevalence of skin diseases and critical shortage of dermatologists. Despite approaching expert-level diagnosis performance, convolutional neural network (ConvNet) adoption in clinical practice is impeded by their limited explainability, and by subjective, expensive explainability validations. We introduce DermX, an end-to-end framework for explainable automated dermatological diagnosis. DermX is a clinically-inspired explainable dermatological diagnosis ConvNet, trained using DermXDB, a 554 image dataset annotated by eight dermatologists with diagnoses, supporting explanations, and explanation attention maps. DermX+ extends DermX with guided attention training for explanation attention maps. Both methods achieve near-expert diagnosis performance, with DermX, DermX+, and dermatologist F1 scores of 0.79, 0.79, and 0.87, respectively. We assess the explanation performance in terms of identification and localization by comparing model-selected with dermatologist-selected explanations, and gradient-weighted class-activation maps with dermatologist explanation maps, respectively. DermX obtained an identification F1 score of 0.77, while DermX+ obtained 0.79. The localization F1 score is 0.39 for DermX and 0.35 for DermX+. These results show that explainability does not necessarily come at the expense of predictive power, as our high-performance models provide expert-inspired explanations for their diagnoses without lowering their diagnosis performance.