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Fungrim entry: 1d3fd7

ddyatan2 ⁣(y,x)=xx2+y2\frac{d}{d y}\, \operatorname{atan2}\!\left(y, x\right) = \frac{x}{{x}^{2} + {y}^{2}}
Assumptions:xRandyRand(x>0ory0)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
RealDerivativeddxf ⁣(x)\frac{d}{d x}\, f\!\left(x\right) Real derivative
Atan2atan2 ⁣(y,x)\operatorname{atan2}\!\left(y, x\right) Two-argument inverse tangent
Powab{a}^{b} Power
RRR\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)))))

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

2020-01-31 18:09:28.494564 UTC