Differentiate the following with respect of `x :(x+1/x)(sqrt(x)+1/(sqrt(x)))`

Explanation

To differentiate the function \( f(x) = \left( x + \frac{1}{x} \right) \left( \sqrt{x} + \frac{1}{\sqrt{x}} \right) \), we will follow these steps:

### Step 1: Simplify the function
First, we need to simplify the expression by multiplying the two parts together.

\[ f(x) = \left( x + \frac{1}{x} \right) \left( \sqrt{x} + \frac{1}{\sqrt{x}} \right) \]
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