Good point. So this is probably one of the reasons why the version I stated isn't used.
It is used, just with the caveat in mind that it may exist when the derivative doesn't. It is usually called the symmetric derivative (https://en.wikipedia.org/wiki/Symmetric_derivative).
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It is used, just with the caveat in mind that it may exist when the derivative doesn't. It is usually called the symmetric derivative (https://en.wikipedia.org/wiki/Symmetric_derivative).