Question

If derivative of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$ w.r.t. $\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)$ at $x=50$ is equal to a and derivative of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$ w.r.t. $\cos ^{-1}\left(\frac{2 x}{1+x^2}\right)$ at $x=-50$ is equal to $b$. Then $(a+b)$ equals

• A. 0
• B. 1
• C. - 1
• D. 2

Answer 1

Answer: (D)

$a = 1 $ and $b = 1$
$\therefore (a + b) = 2. $