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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $y = b\cos \log {\left( {{x \over n}} \right)^n}$, then ${{dy} \over {dx}} = $
  • A
    $ - n\,\,b\sin \log {\left( {{x \over n}} \right)^n}$
  • B
    $n\,\,b\sin \log {\left( {{x \over n}} \right)^n}$
  • ✓
    $\frac{{ - nb}}{x}\sin \log {\left( {\frac{x}{n}} \right)^n}$
  • D
    None of these
✓

Answer

Correct option: C.
$\frac{{ - nb}}{x}\sin \log {\left( {\frac{x}{n}} \right)^n}$
c
(c) $\frac{{dy}}{{dx}} = - b\sin \log {\left( {\frac{x}{n}} \right)^n} \frac{1}{{{{(x/n)}^n}}}\frac{n}{n}{\left( {\frac{x}{n}} \right)^{n - 1}} $

$= - \frac{{nb}}{x}\sin \log {\left( {\frac{x}{n}} \right)^n}$.

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