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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $y = \log {x^x},$ then ${{dy} \over {dx}} = $
  • A
    ${x^x}(1 + \log x)$
  • ✓
    $\log (ex)$
  • C
    $\log \left( {{e \over x}} \right)$
  • D
    None of these
✓

Answer

Correct option: B.
$\log (ex)$
b
(b) $y = \log {x^x} = x\log x$

Differentiating w.r.t. $x,$ we get

$\frac{{dy}}{{dx}} = (1 + \log x) = \log e + \log x = \log (ex)$,   $(\because \log e = 1)$

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