Originally (as far as I know) the number e (ie. 2.71828...) came up in compound interest calculations. For example, if you have 1 dollar, and a compound interest of 100% per year, and the interest is continuously calculated, after one year you'll have exactly e dollars. The generic formula for this is (1+1/n)n, where n is the amount of times compound interest is calculated during the year. As n approaches infinity (which means it's continuously calculated), that formula approaches e. Is the fact that ex is its own derivative just a coincidence, or is there a correlation with the above?