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

InterviewSolution

1.	Find the derivative of `(x^(n)-a^(n))/(x-a)` for some constant a.
Answer» Let `y=(x^(n)-a^(n))/(x-a)` `rArr (dy)/(dx)=(d)/(dx)((x^(n)-a^(n))/(x-a))` `=((xa)(d)/(dx)(x^(n)-a^(n))-(x^(n)-a^(n))(d)/(dx)(x-d))/((x-a)^(2))` `=((x-a)(nx^(n-1)-0)-(x^(n)-a^(n))(d)/(dx)(x-a))/((x-a)^(2))` `=((x-a)(nx^(n-1)-0)-(x^(n)-a^(n))(1-0))/((x-a)^(2))` `=(nx^(n)-anx^(n-1)-x^(n)+a^(n))/((x-a)^(2))`

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