Abstract: This talk will start with a review of Goodwillie calculus and the Taylor tower, and then consider the question of the universal structure that exists on the derivatives of a homotopy functor between given categories. The first step is to describe the operad structure on the derivatives of the identity, and how this operad acts on the derivatives of another functor. Underlying this step is the "chain rule" for Goodwillie derivatives. The second step is to introduce a comonad that describes further structure on the derivatives. This is an example of homotopic descent. I will focus on the examples of functors between the categories of based spaces and spectra, but will try to indicate how the general method could be applied to other categories. This is joint work with Greg Arone.