What is the relationship between [Fréchet derivatives](https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative), [Gateaux derivatives](https://en.wikipedia.org/wiki/Gateaux_derivative) and the usual Euler-Lagrange operator (ELO)? Is the ELO the Fréchet derivative, the Gateaux derivative or does it depends on the context and the theory/lagrangian we consider?