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Display information for equation id:math.1108.174 on revision:1108

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TeX (original user input): 

\partial {{'}_{\nu }}A{{'}^{\mu }}={{\partial }_{\rho }}A{{'}^{\mu }}\partial {{'}_{\nu }}{{x}^{\rho }}={{\partial }_{\rho }}\left( {{\partial }_{\sigma }}x{{'}^{\mu }}{{A}^{\sigma }} \right)\partial {{'}_{\nu }}{{x}^{\rho }}=\partial _{\rho \sigma }^{2}x{{'}^{\mu }}\partial {{'}_{\nu }}{{A}^{\sigma }}+{{\partial }_{\sigma }}x{{'}^{\mu }}\partial {{'}_{\nu }}{{x}^{\rho }}{{\partial }_{\rho }}{{A}^{\sigma }}

TeX (checked): 

\partial {{'}_{\nu }}A{{'}^{\mu }}={{\partial }_{\rho }}A{{'}^{\mu }}\partial {{'}_{\nu }}{{x}^{\rho }}={{\partial }_{\rho }}\left({{\partial }_{\sigma }}x{{'}^{\mu }}{{A}^{\sigma }}\right)\partial {{'}_{\nu }}{{x}^{\rho }}=\partial _{\rho \sigma }^{2}x{{'}^{\mu }}\partial {{'}_{\nu }}{{A}^{\sigma }}+{{\partial }_{\sigma }}x{{'}^{\mu }}\partial {{'}_{\nu }}{{x}^{\rho }}{{\partial }_{\rho }}{{A}^{\sigma }}

LaTeXML (experimental; uses MathML) rendering

MathML (19.677 KB / 2.533 KB) :

∂ A ′ ν = ′ μ ∂ ρ A ∂ ′ μ x ρ ′ ν = ∂ ρ ( ∂ σ x A σ ′ μ ) ∂ x ρ ′ ν = ∂ ρ ⁢ σ 2 x ∂ ′ μ A σ ′ ν + ∂ σ x ∂ ′ μ x ρ ′ ν ∂ ρ A σ fragments superscript subscript 𝐴 𝜈 ′ superscript superscript 𝜇 ′ subscript 𝜌 A superscript superscript 𝜇 ′ superscript subscript superscript 𝑥 𝜌 𝜈 ′ subscript 𝜌 fragments ( subscript 𝜎 x superscript superscript superscript 𝐴 𝜎 𝜇 ′ ) superscript subscript superscript 𝑥 𝜌 𝜈 ′ superscript subscript 𝜌 𝜎 2 x superscript superscript 𝜇 ′ superscript subscript superscript 𝐴 𝜎 𝜈 ′ subscript 𝜎 x superscript superscript 𝜇 ′ superscript subscript superscript 𝑥 𝜌 𝜈 ′ subscript 𝜌 superscript 𝐴 𝜎 {\displaystyle{\displaystyle\partial{{{}^{\prime}}_{\nu}}A{{{}^{\prime}}^{\mu}% }={{\partial}_{\rho}}A{{{}^{\prime}}^{\mu}}\partial{{{}^{\prime}}_{\nu}}{{x}^{% \rho}}={{\partial}_{\rho}}\left({{\partial}_{\sigma}}x{{{}^{\prime}}^{\mu}}{{A% }^{\sigma}}\right)\partial{{{}^{\prime}}_{\nu}}{{x}^{\rho}}=\partial_{\rho% \sigma}^{2}x{{{}^{\prime}}^{\mu}}\partial{{{}^{\prime}}_{\nu}}{{A}^{\sigma}}+{% {\partial}_{\sigma}}x{{{}^{\prime}}^{\mu}}\partial{{{}^{\prime}}_{\nu}}{{x}^{% \rho}}{{\partial}_{\rho}}{{A}^{\sigma}}}} 
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    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle\partial{{{}^{\prime}}_{\nu}}A{{{}^{\prime}}^{\mu}%
}={{\partial}_{\rho}}A{{{}^{\prime}}^{\mu}}\partial{{{}^{\prime}}_{\nu}}{{x}^{%
\rho}}={{\partial}_{\rho}}\left({{\partial}_{\sigma}}x{{{}^{\prime}}^{\mu}}{{A%
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\sigma}^{2}x{{{}^{\prime}}^{\mu}}\partial{{{}^{\prime}}_{\nu}}{{A}^{\sigma}}+{%
{\partial}_{\sigma}}x{{{}^{\prime}}^{\mu}}\partial{{{}^{\prime}}_{\nu}}{{x}^{%
\rho}}{{\partial}_{\rho}}{{A}^{\sigma}}}}</annotation>
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</math>

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∂'νA'μ=∂ρA'μ∂'νxρ=∂ρ(∂σx'μAσ)∂'νxρ=∂ρσ2x'μ∂'νAσ+∂σx'μ∂'νxρ∂ρAσ
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