Differentiate: `(logx)^x+x^(logx)` with respect to `xdot`

Explanation

To differentiate the expression \( ( \log x )^x + x^{\log x} \) with respect to \( x \), we will break it down into two parts and differentiate each part separately.

Let:
\[ y = (\log x)^x + x^{\log x} \]

### Step 1: Differentiate \( u = (\log x)^x \)

1. **Take the natural logarithm of both sides**:
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