Differentiation Question 413
Question: If $ y={\log _{\cos x}}\sin x $ , then $ \frac{dy}{dx} $ is equal to
Options:
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 these
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ y={\log _{\cos x}}\sin x=\frac{\log \sin x}{\log \cos x} $
$ \therefore \frac{dy}{dx}=\frac{\cot x.\log \cos x+(\log \sin x)\tan x}{{{(\log \cos x)}^{2}}} $ .
BETA
