Differentiate w.r.t x , `y = (x^(2)+1)//(x-1) `. Here `u = x^(2) +1, v = x - 1 `

Explanation

To differentiate the function \( y = \frac{x^2 + 1}{x - 1} \) with respect to \( x \), we will use the quotient rule. The quotient rule states that if you have a function in the form \( y = \frac{u}{v} \), then the derivative \( \frac{dy}{dx} \) can be calculated using the formula:

\[ \frac{dy}{dx} = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2} \]

where:
- \( u = x^2 + 1 \)
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