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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
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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