James Serrin, Dale E. Varberg, A General Chain Rule for Derivatives and the Change of Variables Formula for the Lebesgue Integral, The American Mathematical Monthly, Vol. 76, No. 5 (May, 1969), pp.

We prove a chain rule for the Goodwillie calculus of functors from spectra to spectra. We show that the (higher) derivatives of a composite functor FG at a base object X are given by taking the ...