If f(x) = _x ( x), then f'(x) at x = e is - Vidyadip

MCQ

If $f(x) = {\log _x}(\log x),$ then $f'(x)$ at $x = e$ is

A
$e$
✓
${1 \over e}$
C
$1$
D
None of these

✓

Answer

Correct option: B.

${1 \over e}$

b
(b) $f(x) = {\log _x}(\log x) = \frac{{\log (\log x)}}{{\log x}}$

==> $f'(x) = \frac{{\frac{1}{x} - \frac{1}{x}\log (\log x)}}{{{{(\log x)}^2}}} \Rightarrow f'(e) = \frac{{\frac{1}{e} - 0}}{1} = \frac{1}{e}$.

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