Differentiate each function by applying the basic rules of differentiation
`((x^(3)+x^(2)+x+1)/(x^(3)-x^(2)+x-1))`

Explanation

To differentiate the function \( f(x) = \frac{x^3 + x^2 + x + 1}{x^3 - x^2 + x - 1} \), we can use the quotient rule of differentiation. The quotient rule states that if you have a function in the form \( \frac{u}{v} \), then the derivative \( f'(x) \) is given by:

\[ f'(x) = \frac{v \cdot u' - u \cdot v'}{v^2} \]

Where:
- \( u = x^3 + x^2 + x + 1 \)
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