Xth root of X question

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Mike M.

Joined Oct 9, 2007
104

mogadeet

Joined May 1, 2007
19
hey mike

to differentiate f(x) = x^(1/x) recast it as exp[ ln[ x^(1/x) ] ] = exp[ (1/x) ln x]. you then obtain Df(x) = f(x) (1/x^2) (1 - ln x), which is zero iff ln x = 1 iff x=e.

peace
stm

ps: e^(1/e) is transcendental while sqrt(2) is algebraic: not the same number
 
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