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Question #9f557

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Mar 8, 2017

$\frac{1}{x - 1} - \frac{1}{x}$ $1/(x-1)-1/x$ or (equivalently) $\frac{1}{x (x - 1)}$ $1/(x(x-1))$

Explanation:

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

So the derivative is

$\frac{1}{x - 1} - \frac{1}{x}$ $1/(x-1)-1/x$ which can be written $\frac{1}{x (x - 1)}$ $1/(x(x-1))$

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