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Problem 27 Medium Difficulty

Differentiate $ f $ and find the domain of $ f. $

$ f(x) = \frac {x}{1 - \ln (x - 1)} $

Answer

$f^{\prime}(x)$ $=\frac{2 x-1-(x-1) \ln (x-1)}{(x-1)[1-\ln (x-1)]^{2}}$
$\operatorname{Dom}(f)$ $=\left\{x | x>1 \text { and } x-1 \neq e^{1}\right\}=\{x | x>1 \text { and } x \neq 1+e\}=(1,1+e) \cup(1+e, \infty)$

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Video Transcript

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