Easy problem with derivatives

Given that $f(x)=\frac {1}{x}$ and ${f}\prime(x)=-\frac{1}{{x}^{2}}$ it shows that ${f}^{n}(x)={f}^{n-1}\times\frac{-n}{x}$ or in other words, ${f}^{n}(x)={(-1)}^{n}\times\frac{n!}{{x}^{n+1}}$ so operating that we get that the solution is $-\frac{362880}{{x}^{10}}$