Question

If $\text{y = b}\text{cos}\text{log}{\left(\frac{x}{n}\right)}^n,then\frac{dy}{dx}=$

• A. $\frac{-nb\sin \log {\left(x\right)}^n}{x}$
• B. $nb\sin \log {\left(\frac{x}{n}\right)}^n$
• C. $-nb\sin \log {\left(\frac{x}{n}\right)}^n$
• D. None of these

Answer 1

The correct option is A $\frac{-nb\sin \log {\left(x\right)}^n}{x}$

$y=b\cos \log {\left(\frac{x}{n}\right)}^n$

then $y=b\cos \left[n\log \left(\frac{x}{n}\right)\right]$

$y=b\cos [n\log x-n\log n]$

$y=b\cos \left(n\log x\right)-b\cos \left(n\log n\right)$

$\therefore \frac{dy}{dx}=-b\sin \left(n\log x\right).\frac{n}{x}$

$y=-nb\sin \left(\log x^n\right).\frac{1}{x}$