In mobile edge computing (MEC), partial computational offloading can be intelligently investigated to reduce the energy consumption and service delay of user equipment (UE) by dividing a single task into different components. Some of the components execute locally on the UE while the remaining are offloaded to a mobile edge server (MES). In this paper, we investigate the partial offloading technique in MEC using a supervised deep learning approach. The proposed technique, comprehensive and energy efficient deep learning-based offloading technique (CEDOT), intelligently selects the partial offloading policy and also the size of each component of a task to reduce the service delay and energy consumption of UEs. We use deep learning to find, simultaneously, the best partitioning of a single task with the best offloading policy. The deep neural network (DNN) is trained through a comprehensive dataset, generated from our mathematical model, which reduces the time delay and energy consumption of the overall process. Due to the complexity and computation of the mathematical model in the algorithm being high, due to trained DNN the complexity and computation are minimized in the proposed work. We propose a comprehensive cost function, which depends on various delays, energy consumption, radio resources, and computation resources. Furthermore, the cost function also depends on energy consumption and delay due to the task-division-process in partial offloading. None of the literature work considers the partitioning along with the computational offloading policy, and hence, the time and energy consumption due to task-division-process are ignored in the cost function. The proposed work considers all the important parameters in the cost function and generates a comprehensive training dataset with high computation and complexity. Once we get the training dataset, then the complexity is minimized through trained DNN which gives faster decision making with low energy consumptions. Simulation results demonstrate the superior performance of the proposed technique with high accuracy of the DNN in deciding offloading policy and partitioning of a task with minimum delay and energy consumption for UE. More than 70% accuracy of the trained DNN is achieved through a comprehensive training dataset. The simulation results also show the constant accuracy of the DNN when the UEs are moving which means the decision making of the offloading policy and partitioning are not affected by the mobility of UEs.