Differentiation Question 344
Question: $ \frac{d}{dx}{{\cos }^{-1}}\frac{x-{x^{-1}}}{x+{x^{-1}}} $ =
[DSSE 1985; Rookee 1963]
Options:
A) $ \frac{1}{1+x^{2}} $
B) $ \frac{-1}{1+x^{2}} $
C) $ \frac{2}{1+x^{2}} $
D) $
$ $ \frac{-2}{1+x^{2}} $
Show Answer
Answer:
Correct Answer: D
Solution:
Putting $ x=\cot \theta $
$ y={{\cos }^{-1}}( \frac{x-{x^{-1}}}{x+{x^{-1}}} )={{\cos }^{-1}}( \frac{x^{2}-1}{x^{2}+1} ) $
$ ={{\cos }^{-1}}(\cos 2\theta )=2\theta \Rightarrow \frac{dy}{dx}=\frac{-2}{1+x^{2}} $ .
BETA
