ISRO | ISRO CS 2011 | Question 59

n-th derivative of xn is
(A) n xn-1
(B) nn . n!
(C) nxn !
(D) n!

Answer: (D)


f(x) = xn
f'(x) = n.xn-1
f"(x) = n(n-1).xn-2 and so on.
So, nth derivative of f(x) = n(n-1)(n-2)...1.xn-n
=  n(n-1)(n-2)...1.x0
= n!

So, option (D) is correct.

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