Differentiate each function by applying the basic rules of differentiation
`(x)/(1+x^(2))`

Explanation

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

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

where \( u = x \) and \( v = 1 + x^2 \).

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