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\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 (experimentell; verwendet MathML) rendering

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∂ 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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∂ ′ ν A ′ μ = ∂ ρ A ′ μ ∂ ′ ν x ρ = ∂ ρ ( ∂ σ x ′ μ A σ ) ∂ ′ ν x ρ = ∂ ρ σ 2 x ′ μ ∂ ′ ν A σ + ∂ σ x ′ μ ∂ ′ ν x ρ ∂ ρ A σ {\displaystyle \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 }}} 
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    <annotation encoding="application/x-tex">{\displaystyle \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 }}}</annotation>
  </semantics>
</math>

SVG (11.937 KB / 3.587 KB) :

{\displaystyle \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 }}}

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