Derivative of Arccotangent Function

Theorem
Let $x \in \R$.

Let $\operatorname{arccot} x$ be the arccotangent of $x$.

Then:
 * $\dfrac {\mathrm d \left({\operatorname{arccot} x }\right)} {\mathrm d x} = \dfrac {-1} {1 + x^2}$

Also defined as
This result can also be reported as:
 * $\dfrac {\mathrm d \left({\operatorname{arccot} x }\right)} {\mathrm d x} = \dfrac {-1} {x^2 + 1}$