d dx ( _e x)( _a x)] = - Vidyadip

MCQ

${d \over {dx}}({\log _e}x)({\log _a}x)] = $

A
${{{{\log }_a}x} \over x}$
B
${{{{\log }_x}x} \over x}$
C
${{2\log x} \over x}$
✓
${{2{{\log }_a}x} \over x}$

✓

Answer

Correct option: D.

${{2{{\log }_a}x} \over x}$

d
(d) $\frac{d}{{dx}}\left( {{{\log }_e}x.{{\log }_a}x} \right) = \frac{d}{{dx}}\left[ {\log x.\frac{{\log x}}{{\log a}}} \right]$

$ = \frac{{2\log x}}{{x.\log a}} = \frac{{2{{\log }_a}x}}{x}$.

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