Nth Derivative of Reciprocal of Mth Power/Corollary

Theorem

The $n$th derivative of $\dfrac 1 x$ with respect to $x$ is:

$\dfrac {\d^n} {\d x^n} \dfrac 1 x = \dfrac {\paren {-1}^n n!} {x^{n + 1} }$

where $n!$ denotes $n$ factorial.

Proof

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

$\blacksquare$