`tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))`

Explanation

To solve the problem \( y = \tan^{-1}\left(\frac{\sqrt{1+x^2} + \sqrt{1-x^2}}{\sqrt{1+x^2} - \sqrt{1-x^2}}\right) \) and find \( \frac{dy}{dx} \), we can follow these steps:

### Step 1: Substitute \( x = \cos(2\theta) \)

Let \( x = \cos(2\theta) \). Then, we can express \( x^2 \) as \( \cos^2(2\theta) \).

### Step 2: Rewrite the expression

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