If `y=sqrt(x/a)+sqrt(a/x)` , prove that `2x y(dy)/(dx)=(x/a-a/x)`

Explanation

To prove that \( 2xy \frac{dy}{dx} = \frac{x}{a} - \frac{a}{x} \) for the function \( y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}} \), we will follow these steps:

### Step 1: Differentiate \( y \) with respect to \( x \)

Given:
\[ y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}} \]
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