1. The word "redouble your efforts" is an adverb, indicating the increase of multiple, emphasizing the degree of effort several times more than the original. So the meaning of redoubling efforts is to work harder and harder than usual; To redouble one's efforts is a verb, which means to increase the multiple, so the semantics of redoubling one's efforts means to redouble one's efforts on the original basis.

2. In usage, doubled efforts is usually used as a fixed collocation, which means to work harder for something, such as "he studied harder for the exam for a month"; Redouble efforts can be used as a verb phrase or verb plus adverb, which means redoubling efforts on the original basis, for example, "In order to complete the task, he decided to redouble his efforts."