n-th derivative of xn is
2011
n-th derivative of xn is
- A.
n xn-1
- B.
nn . n!
- C.
nxn !
- D.
n!
Attempted by 19 students.
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Correct answer: D
Apply the power rule repeatedly to differentiate x^n. The first derivative is n*x^(n-1), and the second is n*(n-1)*x^(n-2).
After n differentiations, the exponent reaches 0 and the coefficient becomes the product of integers from n down to 1. This equals n!, so the n-th derivative is n!.