Differentiate `tan^(-1)((2x)/(1-x^(2)))` w.r.t. `sin^(-1)((2x)/(1+x^(2))).`

Explanation

To differentiate \( y = \tan^{-1}\left(\frac{2x}{1 - x^2}\right) \) with respect to \( z = \sin^{-1}\left(\frac{2x}{1 + x^2}\right) \), we will use the chain rule.

### Step-by-step Solution:

1. **Identify the functions**:
Let:
\[
u = \tan^{-1}\left(\frac{2x}{1 - x^2}\right)
...