Differentiate the following w.r.t x: sec^-1(x^2 +1)/(x^2 - 1)

Question

Differentiate the following w.r.t x: sec^-1\(\left(\cfrac{\text x^2+1}{\text x^2-1}\right)\)

sec^-1(x² +1)/(x² - 1)

Answer 1

To find: Value of sec^-1\(\left(\cfrac{\text x^2+1}{\text x^2-1}\right)\)

sec^-1(x² +1)/(x² - 1)

The formula used: (i) cos θ  = sin\(\left(\cfrac\pi2-\theta\right)\)

Now, we can see that  sec^-1\(\left(\cfrac{\text x^2+1}{\text x^2-1}\right)\) = π - 2 tan^-1x

Now Differentiating