Right derived functors are a concept in homological algebra that extend the idea of functors to measure how well a functor behaves with respect to exact sequences. They are constructed from a left exact functor by applying a process that involves taking a projective resolution of an object. This allows us to capture information about the "failure" of the functor to be exact. These derived functors provide valuable insights in various areas of mathematics, such as in the study of modules, sheaves, and cohomology. Common examples include the right derived functors of the Hom functor, denoted as Ext, and the derived functors of the tensor product, denoted as Tor.