Find the derivative of `sec^(-1)(1/(2x^2-1))` w.r.t `sqrt(1-x^2)` at `x=1/2`

Explanation

To find the derivative of \( \sec^{-1}\left(\frac{1}{2x^2 - 1}\right) \) with respect to \( \sqrt{1 - x^2} \) at \( x = \frac{1}{2} \), we can follow these steps:

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

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