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Given f(x) = x99. Find f(99). Where f(n) represents the nth differentiation of f(x) with respect to x. 

Given f(x) = x99. Find f(99). Where f(n) represents the nth differentiation of f(x) with respect to x.  Correct Answer 99!

Let f(x) = xn

f’(x) = nxn - 1

f’’(x) = n(n - 1)xn - 2

f’’’(x) = n(n - 1)(n - 2)xn - 3

f’’’’(x) = n(n - 1)(n - 2)(n - 3)xn - 4

………………………………………….

fn(x) = n(n - 1)(n - 2)(n - 3)……………………(n - (n - 1)) xn - n = n!

f(99) = 99!

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