Differentiation Question 293
Question: If $ y={\log _{\sin x}}(\tan x), $ then $ {{( \frac{dy}{dx} )} _{\pi /4}}= $
Options:
A) $ \frac{4}{\log 2} $
B) $ -4\log 2 $
C) $ \frac{-4}{\log 2} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ y=\frac{\log \tan x}{\log \sin x} $
Therefore $ \frac{dy}{dx}=\frac{(\log \sin x)( \frac{{{\sec }^{2}}x}{\tan x} )-(\log \tan x)(\cot x)}{{{(\log \sin x)}^{2}}} $
Therefore $ {{( \frac{dy}{dx} )} _{\pi /4}}=\frac{-4}{\log 2} $ (On simplification).
BETA
