If y = x^x, then dy dx = - Vidyadip

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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