ISRO2011-59

Question

$n$-th derivative of $x^n$ is

• A. $nx^{n-1}$
• B. $n^n.n!$
• C. $nx^n!$
• D. $n!$

Comments

Ans - D. n!

Answer 1

 f(x) = xⁿ 

f'(x) = n x^(n-1) 

f''(x) = n(n-1) x^(n-2) 

f'''(x) = n(n-1)(n-2) x^(n-3) 

fⁿ(x) = n! x^(n-n) , and since n-n = 0, x⁰ =1, 

so fⁿ(x) = n! 

Hence,Option(D)n! is the correct choice.