Differentiation Question 298
Question: The derivative of $ {{\cos }^{-1}}( \frac{1-x^{2}}{1+x^{2}} ) $ w.r.t. $ {{\cot }^{-1}}( \frac{1-3x^{2}}{3x-x^{2}} ) $ is
[Karnataka CET 2003]
Options:
A) 1
B) $ \frac{3}{2} $
C) $ \frac{2}{3} $
D) $ \frac{1}{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ y_1={{\cos }^{-1}}( \frac{1-x^{2}}{1+x^{2}} )=2{{\tan }^{-1}}x $ , $ {{\cot }^{-1}}( \frac{1-3x^{2}}{3x-x^{3}} )=3{{\tan }^{-1}}x\Rightarrow \frac{dy_1}{dy_2}=\frac{( \frac{dy_1}{dx} )}{( \frac{dy_2}{dx} )}=\frac{( \frac{2}{1+x^{2}} )}{( \frac{3}{1+x^{2}} )}=\frac{2}{3} $
BETA
