Differentiate `tan^(-1)((2x)/(1-x^2))` with respect to `cos^(-1)((1-x^2)/(1+x^2))`, if `0 < x < 1` .

Explanation

To differentiate \( u = \tan^{-1}\left(\frac{2x}{1-x^2}\right) \) with respect to \( v = \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) \), we will follow these steps:

### Step 1: Define the functions
Let:
- \( u = \tan^{-1}\left(\frac{2x}{1-x^2}\right) \)
- \( v = \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) \)

### Step 2: Differentiate \( u \) with respect to \( x \)
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