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Display information for equation id:math.12.5 on revision:12
* Page found: Hauptseite (eq math.12.5)
(force rerendering)Occurrences on the following pages:
Hash: 4199c0523e7279134ff729583219e4ce
TeX (original user input):
\mathbf{\operatorname{rot}}\,
\mathbf F(x,y,z) =
\left (\frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z}\right )\mathbf e_x
+
\left (\frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x}\right )\mathbf e_y
+
\left (\frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y}\right )\mathbf e_z
\,.
TeX (checked):
\mathbf {\operatorname {rot} } \,\mathbf {F} (x,y,z)=\left({\frac {\partial F_{z}}{\partial y}}-{\frac {\partial F_{y}}{\partial z}}\right)\mathbf {e} _{x}+\left({\frac {\partial F_{x}}{\partial z}}-{\frac {\partial F_{z}}{\partial x}}\right)\mathbf {e} _{y}+\left({\frac {\partial F_{y}}{\partial x}}-{\frac {\partial F_{x}}{\partial y}}\right)\mathbf {e} _{z}\,.
LaTeXML (experimentell; verwendet MathML) rendering
MathML (0 B / 8 B) :
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SVG (0 B / 8 B) :
MathML (experimentell; keine Bilder) rendering
MathML (3.108 KB / 419 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal" data-mjx-texclass="OP">rot</mi></mrow><mspace width="0.167em"></mspace><mrow data-mjx-texclass="ORD"><mi mathvariant="bold">F</mi></mrow><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo stretchy="false">)</mo><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mi>z</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>y</mi></mrow></mrow></mfrac></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>z</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mrow data-mjx-texclass="ORD"><mi mathvariant="bold">e</mi></mrow><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>z</mi></mrow></mrow></mfrac></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mi>z</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mrow data-mjx-texclass="ORD"><mi mathvariant="bold">e</mi></mrow><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi></mrow></mrow></mfrac></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>y</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mrow data-mjx-texclass="ORD"><mi mathvariant="bold">e</mi></mrow><mrow data-mjx-texclass="ORD"><mi>z</mi></mrow></msub><mspace width="0.167em"></mspace><mo>.</mo></mstyle></mrow></math>
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