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Could someone please distinguish between the Frechet and Gateaux Derivatives and why one is better to use in the Calculus of Variations?

In your response -- if you are so inclined -- please try to avoid the theoretical foundations of this distinction (as I can investigate that by scoping out sources on the internet).

I am hoping here for a SIMPLE and PRACTICAL distinction that I can use in my head as I read about these issues. I am hoping for a dinstintion in words: "We use the Frechet deriviative which came about because we needed Y and it provided an easy out. And then we extend it to the Gateaux derivative in cases where Z or something and it is useful in cases where W... And we use these in directional derivatives which are different because of Q "- kind of thing

You see, for me, a derivative is a derivative and I know how to take a derivative (of a function or of a vector in the case of a directional derivative). My background is not mathematics: it is engineering: and my math education has been deficient, and I am trying to FIRST understand the distinction before I proceed to its theoretical foundation.

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# A Frechet v Gateaux Derivative and the calculus of variations

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