If `y=[(x^(2)+1)/(x+1)]`, then find ` (dy)/(dx)`.

Explanation

To find the derivative of the function \( y = \frac{x^2 + 1}{x + 1} \) with respect to \( x \), we will use the quotient rule of differentiation. The quotient rule states that if you have a function in the form \( y = \frac{u}{v} \), then the derivative \( \frac{dy}{dx} \) is given by:

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

where \( u \) is the numerator and \( v \) is the denominator.

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