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The nth derivatiive of (x+1)^n is...

The `nth` derivatiive of `(x+1)^n` is

A

`(n-1)!`

B

`(n+1)!`

C

`n! `

D

`n[(n +1)]^(n-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `y = (x + 1)^(n)`
` therefore (dy)/(dx) = n (x + 1)^(n-1)`
` (d^(2)y)/(dx^(2)) = n(n-1)(x+1)^(n-2)`
Similarly , `(d^(n) y)/(dx^(n)) = n(n-1)(n-2) ...*2.1 n!`
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