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Find the derivative of (x^(n)-a^(n))/(x-...

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

Text Solution

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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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