# Fungrim entry: 1d3fd7

$\frac{d}{d y}\, \operatorname{atan2}\!\left(y, x\right) = \frac{x}{{x}^{2} + {y}^{2}}$
Assumptions:$x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R} \;\mathbin{\operatorname{and}}\; \left(x > 0 \;\mathbin{\operatorname{or}}\; y \ne 0\right)$
TeX:
\frac{d}{d y}\, \operatorname{atan2}\!\left(y, x\right) = \frac{x}{{x}^{2} + {y}^{2}}

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R} \;\mathbin{\operatorname{and}}\; \left(x > 0 \;\mathbin{\operatorname{or}}\; y \ne 0\right)
Definitions:
Fungrim symbol Notation Short description
RealDerivative$\frac{d}{d x}\, f\!\left(x\right)$ Real derivative
Atan2$\operatorname{atan2}\!\left(y, x\right)$ Two-argument inverse tangent
Pow${a}^{b}$ Power
RR$\mathbb{R}$ Real numbers
Source code for this entry:
Entry(ID("1d3fd7"),
Formula(Equal(RealDerivative(Atan2(y, x), For(y, y, 1)), Div(x, Add(Pow(x, 2), Pow(y, 2))))),
Variables(x, y),
Assumptions(And(Element(x, RR), Element(y, RR), Or(Greater(x, 0), NotEqual(y, 0)))))

## Topics using this entry

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

2021-03-15 19:12:00.328586 UTC