Derivative of Arctangent Function

Theorem
Let $x \in \R$.

Let $\arctan x$ be the arctangent of $x$.

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

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