Derivative of Arctangent Function/Corollary

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

Let $\arctan \left({\dfrac x a}\right)$ be the arctangent of $\dfrac x a$.

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

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

Also see

 * Derivative of $\arcsin \dfrac x a$


 * Derivative of $\arccos \dfrac x a$


 * Derivative of $\operatorname{arccot} \dfrac x a$


 * Derivative of $\operatorname{arcsec} \dfrac x a$


 * Derivative of $\operatorname{arccsc} \dfrac x a$