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

Explanation

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

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

1. **Take the natural logarithm of both sides**:
\[ \log u = (\sin x - \cos x) \log x \]
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