Fungrim entry: 6b8963

\frac{d}{d x}\, \operatorname{atan2}\!\left(y, x\right) = -\frac{y}{{x}^{2} + {y}^{2}}

Assumptions:

x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R} \,\mathbin{\operatorname{and}}\, \left(x \gt 0 \,\mathbin{\operatorname{or}}\, y \ne 0\right)

TeX:

\frac{d}{d x}\, \operatorname{atan2}\!\left(y, x\right) = -\frac{y}{{x}^{2} + {y}^{2}}

x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, y \in \mathbb{R} \,\mathbin{\operatorname{and}}\, \left(x \gt 0 \,\mathbin{\operatorname{or}}\, y \ne 0\right)

Definitions:

Fungrim symbol	Notation	Short description
`Derivative`	$\frac{d}{d z}\, f\!\left(z\right)$	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("6b8963"),
    Formula(Equal(Derivative(Atan2(y, x), Tuple(x, x, 1)), Neg(Div(y, Add(Pow(x, 2), Pow(y, 2)))))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR), Or(Greater(x, 0), Unequal(y, 0)))))

Topics using this entry

Inverse tangent