Differentiate `cos^(-1)((x-x^(-1))/(x+x^(-1)))` w.r.t. x.

Explanation

To differentiate the function \( y = \cos^{-1} \left( \frac{x - x^{-1}}{x + x^{-1}} \right) \) with respect to \( x \), we will follow these steps:

### Step 1: Simplify the Argument of the Inverse Cosine
We start with the expression inside the inverse cosine:
\[ \frac{x - x^{-1}}{x + x^{-1}} = \frac{x - \frac{1}{x}}{x + \frac{1}{x}} = \frac{\frac{x^2 - 1}{x}}{\frac{x^2 + 1}{x}} = \frac{x^2 - 1}{x^2 + 1} \]
Thus, we can rewrite \( y \) as:
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