Others have answered how it was discovered but I’d like to point out that it may be easier to think of it as “defined” instead of discovered. There are several ways e is defined and I think the easiest way to understand is that f(x)= e^x is defined as a function where the slope is always equal to f(x). That is, the derivative of e^x is e^x. With that definition you can calculate the value of e.
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