Differentiate the following w.r.t. x:`x^(xcosx)+(x^2+1)/(x^2-1)`

Explanation

To differentiate the function \( y = x^{x \cos x} + \frac{x^2 + 1}{x^2 - 1} \) with respect to \( x \), we will break this into two parts: \( u = x^{x \cos x} \) and \( v = \frac{x^2 + 1}{x^2 - 1} \). We will find the derivatives \( \frac{du}{dx} \) and \( \frac{dv}{dx} \) separately and then combine them.

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

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