Derivatives in first year calculus Gateaux Derivatives Frechet Derivatives Covariant Derivatives Lie Derivatives Exterior Derivatives Material Derivatives So, I learn about Gateaux and Frechet when studying calculus of variations I learn about Covariant, Lie and Exterior when studying calculus on manifolds I learn about Material derivatives when studying fluid mechanics But I would have never thought there would be so many. Is this about all there is? May I ask if someone can categorize these? When are they used? How are they used? Are there more? Can you possibly create a table? Are there subsets of each other? Are some a manifestation of only physics or engineering or math? Can anyone bring order out of this chaos for me?