Find `(dy)/(dx)` in the following:`y=cos^(-1)((1-x^2)/(1+x^2)),0 < x < 1`

Explanation

To find \(\frac{dy}{dx}\) for the function \(y = \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right)\), we can follow these steps:

### Step 1: Substitute \(x\) with \(\tan(\theta)\)
Let \(x = \tan(\theta)\). Then, we can express \(1 - x^2\) and \(1 + x^2\) in terms of \(\theta\):
\[ 1 - x^2 = 1 - \tan^2(\theta) = \frac{\cos^2(\theta) - \sin^2(\theta)}{\cos^2(\theta)} = \frac{\cos(2\theta)}{\cos^2(\theta)} \]
\[
...