Derivative of Arctangent Function

Theorem
Let $x \in \R$.

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

Then:
 * $\dfrac {\map \d {\arctan x} } {\d x} = \dfrac 1 {1 + x^2}$

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

Also see

 * Derivative of Arcsine Function
 * Derivative of Arccosine Function
 * Derivative of Arccotangent Function
 * Derivative of Arcsecant Function
 * Derivative of Arccosecant Function