# Fungrim entry: a4eb86

$\operatorname{atan}''(z) = -\frac{2 z}{{\left(1 + {z}^{2}\right)}^{2}}$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, i z \notin \left(-\infty, -1\right] \cup \left[1, \infty\right)$
TeX:
\operatorname{atan}''(z) = -\frac{2 z}{{\left(1 + {z}^{2}\right)}^{2}}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, i z \notin \left(-\infty, -1\right] \cup \left[1, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Derivative$\frac{d}{d z}\, f\!\left(z\right)$ Derivative
Atan$\operatorname{atan}\!\left(z\right)$ Inverse tangent
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
ConstI$i$ Imaginary unit
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Infinity$\infty$ Positive infinity
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Source code for this entry:
Entry(ID("a4eb86"),
Formula(Equal(Derivative(Atan(z), Tuple(z, z, 2)), Neg(Div(Mul(2, z), Pow(Add(1, Pow(z, 2)), 2))))),
Variables(z),
Assumptions(And(Element(z, CC), NotElement(Mul(ConstI, z), Union(OpenClosedInterval(Neg(Infinity), -1), ClosedOpenInterval(1, Infinity))))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC