Differentiate the functions given w.r.t. x:
`(x+1/x)^x+x^((1+1/x))`

Explanation

To differentiate the function \( y = \left( x + \frac{1}{x} \right)^x + x^{\left( 1 + \frac{1}{x} \right)} \) with respect to \( x \), we will break it down into two parts and differentiate each part separately.

### Step 1: Define the function
Let:
\[ y_1 = \left( x + \frac{1}{x} \right)^x \]
\[
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