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$f(x) = frac{x log x}{1 + log x}$ $f'(x) = frac{(1cdot log x + xcdot 1/x)cdot (1 + log x) – (x log x) cdot 1/x}{(1 + log x)^2} =$ $frac{(log x + 1)^2 – log x}{(1 + log x)^2} =$ $1 – frac{log x}{(1 + log x)^2}$
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