Derivative of Arctangent Function/Corollary

Corollary to Derivative of Arctangent Function
Let $x \in \R$.

Let $\map \arctan {\dfrac x a}$ denote the arctangent of $\dfrac x a$.

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

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

Also see

 * Derivative of $\arcsin \dfrac x a$


 * Derivative of $\arccos \dfrac x a$


 * Derivative of $\arccot \dfrac x a$


 * Derivative of $\arcsec \dfrac x a$


 * Derivative of $\arccsc \dfrac x a$