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Calculus/Derivatives of e^x and ln e

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Gary Scheidegger wrote at 2015-07-22 04:51:56
The rule (e^f(x))' = f'(x) e^f(x) is a special form of the more general rule Dx(g(f(x)) = Dx(f(x))Df(g(x)), where Dx is the derivative with respect to x and Df is the derivative with respect to f, and f and g are both functions.  Thus to say (e^f(x))' = f'(x) e^f(x) presupposes that Dx e^x = e^x, or in this case Df e^f(x) = e^f(x).



Indeed one, but by no means only, way of DEFINING e is as the unique positive number such that Dx(e^x) = e^x


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