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taking the derivative of (1+1/x)^lnx
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\[(1+\frac{ 1 }{ x })^{\ln x}\]
take the log, take the derivative, then multiply by this again
\[(1+\frac{1}{x})\ln(\ln(x))\] is when you get when you take the log then take the derivative using product and chain rule, then multiply your result by \[(1+\frac{1}{x})^{\ln(x)}\]
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