Q. If $y = \log_{\cos x}\sin{x,then\frac{dy}{dx}\ }is\ equal\ to\$
A) $\frac{(\cot{x\log{\cos{x + \tan{x\log{\sin{x)}}}}}}}{{(\log{\cos{x)}}}^{2}}$
B) $\frac{(\tan{x\log{\cos{x + \cot{x\log{\sin{x)}}}}}}}{{(\log{\cos{x)}}}^{2}}$
C) $\frac{(\cot{x{log\ cos}{x + \tan{x\log{\sin{x)}}}}}}{{(\log{\sin{x)}}}^{2}}$
D) None of the above
Explanation
(a)
Given, $y = \frac{\log{\sin x}}{\log{\cos x}}$
$\ \Rightarrow \ \frac{dy}{dx} = \frac{\cot{x\log{\cos{x + \tan{x\log{\sin x}}}}}}{{(\log{\cos{x)}}}^{2}}\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.