Differentiate `tan^(-1)((2a^x)/(1-a^(2x))),\ \ a >1,\ -oo

Explanation

Solution:

Let ax = tanθ

Now

Solution:

`y=\tan ^{-1}\{\frac{\sqrt{1+\tan ^{2} \theta}-1}{\tan \theta}\}`

Using` \sec ^{2} \theta=1+\tan ^{2} \theta`

`y=\tan ^{-1}\{\frac{\sqrt{\sec ^{2} \theta}-}{\tan \theta}.`

`y=\tan ^{-1}\{\frac{\sec \theta-1}{\tan \theta}\} `

...