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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.

A

1

B

0

C

`1/2`

D

Does not exist

Text Solution

Verified by Experts

The correct Answer is:
d
Given, `f(x) = (x^(n)-a^(n))/(x-a)`
`therefore f^(')(x) = ((x-a)nx^(n-1)-(x^(n)-a^(n))(1))/(x-a)^(2)` [by quotient rule]
`rArr f^(')(x)= (nx^(n-1)(x-a)-x^(n)+a^(n))/(x-a)^(2)`
Now, `f^(')a=(na^(n-1)(0)-a^(n)+a^(n))/(x-a)^(2)`
`rArr f^(')(a) = 0/0`
So, `f^(')a` does not exist,
Since, f(x) is not defined at x=a
Hence, `f^(')(x)` at x=a does not exist.
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  17. If f(x)=1+x+(x^2)/2++(x^(100))/(100), then f^(prime)(1) is equal to

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

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