To defeat the Exponential Function, Ash tried to apply a mathematical operator to it, but it stayed the same. Which operator could it be?
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Relevant wiki: Derivatives of Exponential Functions
d x d e x = e x so the operation was differentiation.
The other operations are not correct.
Square root of only 0 and 1 is the same as the number itself.
Indefinite integral of e x is e x + C which need not be e x itself.