If y = b ( x n )^n , then dy dx = - Vidyadip

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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