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Many integrals are either very complicated or in some cases impossible? However, I have not yet seen derivatives that are very difficult or cannot be solved for. Does anyone have an example of a derivative that cannot be solved through standard techniques?

Edit: I mean in one variable.

mtheorylord
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  • Oh, sorry. I meant in one variable. – mtheorylord Nov 01 '16 at 01:26
  • The reason that derivatives are usually easy is the chain rule. You'd have to find a function which can't be represented as the product/ composition of elementary functions. –  Nov 01 '16 at 01:27
  • Yes, that is the problem also logarithmic and implicit derivatives usually make things very easy too. – mtheorylord Nov 01 '16 at 01:28
  • How about the Cantor function? –  Nov 01 '16 at 01:34
  • Interesting, as a hint, what definition of the cantor function should I use, because the Wikipedia "base 3 to base 2" looks sketchy and hard to use. – mtheorylord Nov 01 '16 at 01:38
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    That probably is the best definition to figure it out. Basically you have to recognize that the Cantor function is constant a lot. So the derivative will be zero at each of the places where it's not undefined. –  Nov 01 '16 at 01:53
  • Related: http://math.stackexchange.com/questions/20578/why-is-integration-so-much-harder-than-differentiation and http://mathoverflow.net/a/16702/3092 – symplectomorphic Nov 01 '16 at 02:53
  • Perhaps this is one of those things that are hard to reverse, like multiplication and factoring. Thanks for the links. – mtheorylord Nov 02 '16 at 03:32

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