Find the derivative of `(x^n-a^n)/(x-a)`for some constant a.

Explanation

To find the derivative of the function \( f(x) = \frac{x^n - a^n}{x - a} \), we will apply the quotient rule. The quotient rule states that if you have a function in the form of \( \frac{u}{v} \), then the derivative \( f'(x) \) is given by:

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

where \( u = x^n - a^n \) and \( v = x - a \).

...