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Mathematics
General Math
What is significance of eulers number
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[QUOTE="FactChecker, post: 5910621, member: 500115"] It is the only number, a, where d/dx (a[SUP]x[/SUP]) = a[SUP]x[/SUP]. Any other number requires an "e-related" multiplier (like d/dx (2[SUP]x[/SUP]) = ln(2) ⋅ 2[SUP]x[/SUP]). So it is the simplest exponential function when it comes to derivatives. Furthermore, the others (like 2[SUP]x[/SUP] = e[SUP]ln(2)⋅x[/SUP]) are very easy to write in terms of e, so e[SUP]x[/SUP] is the most basic exponential function. Likewise, its inverse function, ln(x), has a very simple derivative, 1/x, whereas derivatives of logarithms to any other base require an "e-related" multiplier. As the link in [USER=618222]@scottdave[/USER] 's post indicates, there are a lot of nice things about e[SUP]z[/SUP] in the complex plane. [/QUOTE]
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What is significance of eulers number
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