Differentiation Question 349

Question: $ n^{th} $ derivative of $ {x^{n+1}} $ is

Options:

A) $ (n+1)!x $

B) $ (n+1)! $

C) $ n!x $

D) $ n! $

Show Answer

Answer:

Correct Answer: A

Solution:

Let $ y={x^{n+1}}; $ then $ y_1=(n+1)x^{n} $

$ y_2=n(n+1){x^{n-1}} $

$ y_3=n(n+1)(n-1){x^{n-2}} $

………………………………. …………………………….. $ y _{n}=(n+1)!x $ .