1. The problem statement, all variables and given/known data Consider the map F: C0([a,b],Rn) --> R, F([tex]\phi[/tex])=[tex]\int\phi(t)\phi(t)[/tex]dt (This is the integral from a to b). Write F as a composition of three maps, each of which is linear or bilinear. Then use the chain rule and generalized product rule to compute DF([tex]\phi[/tex]). 2. Relevant equations 3. The attempt at a solution The only maps I could think of would be something like this: [tex]\phi[/tex]: [a,b] --> Rn A: C0([a,b],Rn) --> C0([a,b],Rn) And then maybe I would need a map for [tex]\phi[/tex][tex]\phi[/tex]? But I'm not sure what that would be or if that's even correct. I'm not even sure that I am on the right track at all with the maps. Does anyone have any ideas? Is it possible that F is one of the three maps? So that the composition becomes F of A of phi?