If y = log_{cos x} sin x,then frac{dy}{dx} is | vedclass

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(A) Given,$y = \log_{\cos x} \sin x = \frac{\log \sin x}{\log \cos x}$.Applying the quotient rule $\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v u

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$\frac{\cot x \log \cos x + 	an x \log \sin x}{(\log \cos x)^2}$

Vedclass · Answer

(A) Given,$y = \log_{\cos x} \sin x = \frac{\log \sin x}{\log \cos x}$.Applying the quotient rule $\frac{d}{dx} \left( \frac{u}{v} ight) = \frac{v u' - u v'}{v^2}$,where $u = \log \sin x$ and $v = \log \cos x$.Then $u' = \frac{1}{\sin x} \cdot \cos x = \cot x$ and $v' = \frac{1}{\cos x} \cdot (-\sin x) = -	an x$.$\frac{dy}{dx} = \frac{(\log \cos x)(\cot x) - (\log \sin x)(-	an x)}{(\log \cos x)^2}$.$\frac{dy}{dx} = \frac{\cot x \log \cos x + 	an x \log \sin x}{(\log \cos x)^2}$.

If $y = \log_{\cos x} \sin x$,then $\frac{dy}{dx}$ is equal to

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