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Question
Find the derivative of `(x^n - a^n)/(x -a)` for some constant a.
Solution
Let `f(x) = (x^n - a^n)/(x - a)`
= `f'(x) = d/(dx) ((x^n - a^n)/(x - a))`
∴ `f'(x) = (|d/dx(x^n - a^n)|(x - a) - (x^n - a^n) d/dx (x - a))/(x - a)^2`
= `(nx^(n - 1)(x -a) - (x^n - a^n). 1)/(x - a)^2`
= `(nx^n - nax^(n - 1) - x^n + a^n)/(x - a)^2`
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