Differentiate the following w.r.t. x:
`(logx)^x+x^(logx)`

Explanation

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

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

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