Derivative of Composite Function/Examples/Reciprocal of Arctangent of x

Example of Derivative of Composite Function

 * $\map {\dfrac \d {\d x} } {\dfrac 1 {\arctan x} } = -\dfrac 1 {\paren {1 + x^2} \arctan^2 x}$

Proof
Let $u = \arctan x$.

Let $y = u^{-1}$.

Thus we have:
 * $y = \dfrac 1 {\arctan x}$

and so: