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Providing prognostic information at the time of cancer diagnosis has important implications for treatment and monitoring. Although cancer staging, histopathological assessment, molecular features, and clinical variables can provide useful prognostic insights, improving risk stratification remains an active research area. We developed a deep learning system (DLS) to predict disease specific survival across 10 cancer types from The Cancer Genome Atlas (TCGA). We used a weakly-supervised approach without pixel-level annotations, and tested three different survival loss functions. The DLS was developed using 9,086 slides from 3,664 cases and evaluated using 3,009 slides from 1,216 cases. In multivariable Cox regression analysis of the combined cohort including all 10 cancers, the DLS was significantly associated with disease specific survival (hazard ratio of 1.58, 95% CI 1.28-1.70, p<0.0001) after adjusting for cancer type, stage, age, and sex. In a per-cancer adjusted subanalysis, the DLS remained a significant predictor of survival in 5 of 10 cancer types. Compared to a baseline model including stage, age, and sex, the c-index of the model demonstrated an absolute 3.7% improvement (95% CI 1.0-6.5) in the combined cohort. Additionally, our models stratified patients within individual cancer stages, particularly stage II (p = 0.025) and stage III (p<0.001). By developing and evaluating prognostic models across multiple cancer types, this work represents one of the most comprehensive studies exploring the direct prediction of clinical outcomes using deep learning and histopathology images. Our analysis demonstrates the potential for this approach to provide significant prognostic information in multiple cancer types, and even within specific pathologic stages. However, given the relatively small number of cases and observed clinical events for a deep learning task of this type, we observed wide confidence intervals for model performance, thus highlighting that future work will benefit from larger datasets assembled for the purposes for survival modeling.