The derivative of f(x)=1xf(x) = \frac{1}{x}f(x)=x1 is −x−2-x^{-2}−x−2. What is the nnn-th derivative?
(−1)nn!x−(n+1)(-1)^n n! x^{-(n+1)}(−1)nn!x−(n+1)
n!x−(n+1)n! x^{-(n+1)}n!x−(n+1)
(−1)n+1n!x−n(-1)^{n+1} n! x^{-n}(−1)n+1n!x−n
(−1)n(n−1)!x−n(-1)^n (n-1)! x^{-n}(−1)n(n−1)!x−n