There are so many available bases. Why is the strange number e preferred over all else?
Of course one could integrate 1x and see this. But is there more to the story?
Answer
Differentiation and integration is precisely why it is considered natural, but not just because
∫1xdx=lnx
ex has the two following nice properties
ddxex=ex
∫exdx=ex+c
If we looked at ax instead, we would get:
ddxax=ddxexln(a)=ln(a)⋅ax
∫axdx=∫exln(a)dx=axln(a)+c
So e is vital to the integration and differentiation of exponentials.
Attribution
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