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Display information for equation id:math.224637.27 on revision:224637

* Page found: Del (eq math.224637.27)

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Hash: c889fb06f98d9f57203a80d613fd8e8e

TeX (original user input): 

\nabla(\vec u \cdot \vec v) = \vec u \times (\nabla \times \vec v) + \vec v \times (\nabla \times \vec u) + ( \vec u \cdot \nabla) \vec v + (\vec v \cdot \nabla )\vec u

TeX (checked): 

\nabla ({\vec {u}}\cdot {\vec {v}})={\vec {u}}\times (\nabla \times {\vec {v}})+{\vec {v}}\times (\nabla \times {\vec {u}})+({\vec {u}}\cdot \nabla ){\vec {v}}+({\vec {v}}\cdot \nabla ){\vec {u}}

LaTeXML (experimental; uses MathML) rendering

MathML (11.194 KB / 1.485 KB) :

∇ ⁡ ( u → ⋅ v → ) = u → × ( ∇ × v → ) + v → × ( ∇ × u → ) + ( u → ⋅ ∇ ) ⁢ v → + ( v → ⋅ ∇ ) ⁢ u → ∇ ⋅ → 𝑢 → 𝑣 → 𝑢 ∇ → 𝑣 → 𝑣 ∇ → 𝑢 ⋅ → 𝑢 ∇ → 𝑣 ⋅ → 𝑣 ∇ → 𝑢 {\displaystyle\nabla({\vec{u}}\cdot{\vec{v}})={\vec{u}}\times(\nabla\times{% \vec{v}})+{\vec{v}}\times(\nabla\times{\vec{u}})+({\vec{u}}\cdot\nabla){\vec{v% }}+({\vec{v}}\cdot\nabla){\vec{u}}} 
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SVG (MathML can be enabled via browser plugin) rendering

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∇ ( u → ⋅ v → ) = u → × ( ∇ × v → ) + v → × ( ∇ × u → ) + ( u → ⋅ ∇ ) v → + ( v → ⋅ ∇ ) u → {\displaystyle \nabla ({\vec {u}}\cdot {\vec {v}})={\vec {u}}\times (\nabla \times {\vec {v}})+{\vec {v}}\times (\nabla \times {\vec {u}})+({\vec {u}}\cdot \nabla ){\vec {v}}+({\vec {v}}\cdot \nabla ){\vec {u}}} 
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    <annotation encoding="application/x-tex">{\displaystyle \nabla ({\vec {u}}\cdot {\vec {v}})={\vec {u}}\times (\nabla \times {\vec {v}})+{\vec {v}}\times (\nabla \times {\vec {u}})+({\vec {u}}\cdot \nabla ){\vec {v}}+({\vec {v}}\cdot \nabla ){\vec {u}}}</annotation>
  </semantics>
</math>

SVG (6.811 KB / 2.164 KB) :

{\displaystyle \nabla ({\vec {u}}\cdot {\vec {v}})={\vec {u}}\times (\nabla \times {\vec {v}})+{\vec {v}}\times (\nabla \times {\vec {u}})+({\vec {u}}\cdot \nabla ){\vec {v}}+({\vec {v}}\cdot \nabla ){\vec {u}}}

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