d dx _ x (1/x) is equal to - Vidyadip

Question

${d \over {dx}}{\log _{\sqrt x }}(1/x)$ is equal to

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Answer

d
(d) $f(x) = {\log _{\sqrt x }}\left( {\frac{1}{x}} \right) $

$= \frac{{\log \left( {\frac{1}{x}} \right)}}{{\log \sqrt x }} $

$= \frac{{( - 1)\log x}}{{(1/2)\,\log x}} = - 2$

==> $f'(x) = 0$.

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