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

Inverse tangent