The ability in rapidly learning and adapting to evolving user needs is key to modern business success. Existing methods are based on text mining and machine learning techniques to analyze user comments and feedback, and often constrained by heavy reliance on manually codified rules or insufficient training data. Multitask learning (MTL) is an effective approach with many successful applications, with the potential to address these limitations associated with requirements analysis tasks. In this paper, we propose a deep MTL-based approach, DEMAR, to address these limitations when discovering feature requests from massive issue reports and annotating the sentences in support of automated requirements analysis. DEMAR consists of three main phases: 1) data augmentation phase, for data preparation and allowing data sharing beyond single-task learning; 2) model construction phase, for constructing the MTL-based model for requirements discovery and requirements annotation tasks; and 3) model training phase, enabling eavesdropping by shared loss function between the two related tasks. Evaluation results from eight open-source projects show that, the proposed multitask learning approach outperforms two state-of-the-art approaches (FRA and CNC) and six common machine learning algorithms across both requirements discovery and requirements annotation tasks, i.e., with a precision of 91% and a recall of 83% for requirements discovery task, and overall accuracy of 83% for requirements annotation task. The proposed approach provides a novel and effective way to jointly learn two related requirements analysis tasks. We believe that it also sheds light on further directions in exploring the application of multitask learning in solving other related software engineering problems.