What Are the Different Types of Derivatives in Calculus?

In summary, derivatives in first year calculus include Gateaux, Frechet, Covariant, Lie, Exterior, and Material derivatives. These are used in calculus of variations, calculus on manifolds, and fluid mechanics. They can be categorized as continuous generalizations and there may be subsets of each other. They are not limited to a specific field and can be used in physics, engineering, and mathematics. However, fully understanding and organizing these derivatives may require more time and effort.
  • #1
observer1
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  1. Derivatives in first year calculus
  2. Gateaux Derivatives
  3. Frechet Derivatives
  4. Covariant Derivatives
  5. Lie Derivatives
  6. Exterior Derivatives
  7. 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?
 
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I'm inclined to make an Insight out of it. Looks like an invitation to a small essay.
 
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  • #3
fresh_42 said:
I'm inclined to make an Insight out of it. Looks like an invitation to a small essay.

Please...
 
  • #4
observer1 said:
Please...
But this takes some time. Maybe someone is faster here. But I doubt there is a short answer, except perhaps: continuous generalizations.
 

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