Applications Of Derivatives Question 189
Question: If $ y={{\cot }^{-1}}{{(\cos 2x)}^{1/2}} $ , then the value of $ \frac{dy}{dx} $ at $ x=\frac{\pi }{6} $ will be
[IIT 1992]
Options:
A) $ {{( \frac{2}{3} )}^{1/2}} $
B) $ {{( \frac{1}{3} )}^{1/2}} $
C) $ {{(3)}^{1/2}} $
D) $ {{(6)}^{1/2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dy}{dx}=\frac{-1}{1+\cos 2x}\times \frac{1}{2\sqrt{\cos 2x}}\times -2\sin 2x=\frac{\tan x}{\sqrt{\cos 2x}} $
$ \Rightarrow {{( \frac{dy}{dx} )}_{x=\pi /6}}=\frac{1/\sqrt{3}}{\sqrt{1/2}}=\sqrt{\frac{2}{3}} $ .
BETA
