The exponential of the derivative translates a function 𝑓(𝑥) by an amount εpic.twitter.com/mwQ1aLpOHt
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That much is clear.
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That is what I thought. It follows from lots of other results, but itself is a bit of an orphan.
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Once I used related ideas to come up with the series expansion for the Lambert W function (the inverse of xe^x) The main idea is letting A=DE, where D=d/dx and E=e^D is the shift operator, and then coming up with an analogue of Taylor's theorem for A instead of D
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