If `y=sqrt(x)+1/(sqrt(x)),p rov et h a t2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))`

Explanation

To prove that \( 2x \frac{dy}{dx} = \sqrt{x} - \frac{1}{\sqrt{x}} \) given \( y = \sqrt{x} + \frac{1}{\sqrt{x}} \), we will follow these steps:

### Step 1: Differentiate \( y \)
Given:
\[ y = \sqrt{x} + \frac{1}{\sqrt{x}} \]
We can rewrite \( \sqrt{x} \) as \( x^{1/2} \) and \( \frac{1}{\sqrt{x}} \) as \( x^{-1/2} \). Thus,
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