Nth Derivative of Reciprocal of Mth Power/Corollary

Theorem
The $n$th derivative of $\dfrac 1 x$ w.r.t. $x$ is:
 * $\dfrac {\mathrm d^n} {\mathrm d x^n} \dfrac 1 x = \dfrac {\left({-1}\right)^n n!} {x^{n + 1}}$

where $n!$ denotes $n$ factorial.

Proof
Follows directly from Nth Derivative of Reciprocal of Mth Power by putting $m = 1$.