I'm reading the book of Drabek, Milota - Methods of Nonlinear Analysis, and at page 121, they state:
but I can't manage to find such counterexample. For clarity the Gateaux derivative is defined in this way:
I need some kind of hints about how to build such counterexample because I'm like going nowhere with my trials. According to me $f$ and $g$ can't be continuous, otherwise G-derivative would be Frechét-derivative and for this kind of derivative the chain rule holds. It is sufficient requiring that only one function is non-continuos?