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Fungrim entry: 6b8963

ddxatan2 ⁣(y,x)=yx2+y2\frac{d}{d x}\, \operatorname{atan2}\!\left(y, x\right) = -\frac{y}{{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 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 > 0 \,\mathbin{\operatorname{or}}\, y \ne 0\right)
Definitions:
Fungrim symbol Notation Short description
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) 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("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)))))

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

2019-09-20 18:07:53.062439 UTC