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TeX (original user input): 

\begin{align}
  & d{{s}^{2}}={{\eta }_{\mu \nu }}\partial {{'}_{\alpha }}{{x}^{\mu }}\partial {{'}_{\beta }}{{x}^{\nu }}dx{{'}^{\alpha }}dx{{'}^{\beta }} \\
 & =g{{'}_{\mu }}_{\nu }dx{{'}^{\mu }}dx{{'}^{\nu }}
\end{align}

TeX (checked): 

{\begin{aligned}&d{{s}^{2}}={{\eta }_{\mu \nu }}\partial {{'}_{\alpha }}{{x}^{\mu }}\partial {{'}_{\beta }}{{x}^{\nu }}dx{{'}^{\alpha }}dx{{'}^{\beta }}\\&=g{{'}_{\mu }}_{\nu }dx{{'}^{\mu }}dx{{'}^{\nu }}\end{aligned}}

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MathML (17.072 KB / 2.088 KB) :

d s 2 = η μ ⁢ ν ∂ x μ ′ α ∂ x ν ′ β d x d ′ α x β ′ = g ν ′ μ d x d ′ μ x ν ′ missing-subexpression fragments d superscript 𝑠 2 subscript 𝜂 𝜇 𝜈 superscript subscript superscript 𝑥 𝜇 𝛼 ′ superscript subscript superscript 𝑥 𝜈 𝛽 ′ d x superscript superscript 𝑑 𝛼 ′ x superscript superscript absent 𝛽 ′ missing-subexpression fragments g superscript subscript 𝜈 𝜇 ′ d x superscript superscript 𝑑 𝜇 ′ x superscript superscript absent 𝜈 ′ {\displaystyle{\displaystyle\begin{aligned} &\displaystyle d{{s}^{2}}={{\eta}_% {\mu\nu}}\partial{{{}^{\prime}}_{\alpha}}{{x}^{\mu}}\partial{{{}^{\prime}}_{% \beta}}{{x}^{\nu}}dx{{{}^{\prime}}^{\alpha}}dx{{{}^{\prime}}^{\beta}}\\ &\displaystyle=g{{{}^{\prime}}_{\mu}}_{\nu}dx{{{}^{\prime}}^{\mu}}dx{{{}^{% \prime}}^{\nu}}\end{aligned}}}

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MathML (1.553 KB / 365 B) :

ds2=ημν∂'αxμ∂'βxνdx'αdx'β=g'μνdx'μdx'ν

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Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“