I had this question for a long time.
We always use it in differentiation,Integration , Logarithms ..etc.
What is its origin ?
What unique qualities does it have over other real numbers?
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2$e=\lim\limits_{n\to\infty}\sqrt[n]{LCM(1,2,3,\ldots,n)}$ – Lucian Oct 22 '15 at 11:12
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It can be shown that $\frac{d}{dx}a^x = ka^x$. When $a=e$, $k=1$. – John Joy Oct 22 '15 at 13:23