Differentiate `x^(xcosx)+(x^2+1)/(x^2-1)` with respect to `x` .

Explanation

To differentiate the function \( f(x) = x^{x \cos x} + \frac{x^2 + 1}{x^2 - 1} \) with respect to \( x \), we will break it down into two parts: \( y = x^{x \cos x} \) and \( z = \frac{x^2 + 1}{x^2 - 1} \).

### Step 1: Differentiate \( y = x^{x \cos x} \)

1. **Take the natural logarithm of both sides**:
\[ \ln y = x \cos x \cdot \ln x \]
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