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18-04-2018
Mathematics

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18-04-2018

Define z = ln(x). Then
y = z^z
y' = z^z * (z')*(1 +ln(z))
Since
z' = 1/x
You have
y' = ln(x)^ln(x) * (1/x) * (1 +ln(ln(x))

Evaluated at x=e, this becomes
y'(e) = 1^1 * (1/e) * (1 +ln(1))
y'(e) = 1/e

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