On the wikipedia page "Generalizations of derivative" the author mentions: *" in Finsler geometry, one studies spaces which look locally like Banach spaces. Thus one might want a derivative with some of the features of a functional derivative and the covariant derivative."*


My question is what does this derivative look like, explicity (for a Finsler manifold over a general Banach space)?


Can someone provide a reference also, much appreciated. 



Reference: Finsler Derivative?
Chapter 2 in Bao, Chern, Shen: *An Introduction to Riemann-Finsler Geometry* may give you the answer.


