MCQ
${d \over {dx}}({x^{{{\log }_e}x}}) = $
- ✓$2{x^{({{\log }_e}x - 1)}}.{\log _e}x$
- B${x^{({{\log }_e}x - 1)}}$
- C${2 \over x}{\log _e}x$
- D${x^{({{\log }_e}x - 1)}}.{\log _e}x$
✓
Answer
Correct option: A.
$2{x^{({{\log }_e}x - 1)}}.{\log _e}x$
a
(a) Let $y = {x^{{{\log }_e}x}}$
(a) Let $y = {x^{{{\log }_e}x}}$
==> ${\log _e}y = {\log _e}x{\log _e}x = {({\log _e}x)^2}$
==> $\frac{1}{y}\frac{{dy}}{{dx}} = 2{\log _e}x.\frac{1}{x}$
$\therefore \frac{{dy}}{{dx}} = 2{x^{({{\log }_e}x - 1)}}{\log _e}x$.
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