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Find the derivative of $ \large\frac{x^n-a^n}{x-a}$ for some constant $a$

1 Answer

Let $f(x) = \large\frac{x^n-a^n}{x-a}$
$ \Rightarrow f'(x) = \large\frac{d}{dx}$$ \bigg(\large\frac{x^n-a^n}{x-a}\bigg)$
By quotient rule,
$ f'(x) = \large\frac{(x-a) \large\frac{d}{dx}(x^n-a^n)-(x^n-a^n)\large\frac{d}{dx}(x-a)}{(x-a)^2}$
$ = \large\frac {(x-a)(nx^{n-1}-0)-(x^n-a^n)}{(x-a)^2}$
$ = \large\frac{nx^n-anx^{n-1}-x^n+a^n}{(x-a)^2}$
answered Apr 9, 2014 by thanvigandhi_1
 

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