Jump to navigation Jump to search

General

Display information for equation id:math.224637.5 on revision:224637

* Page found: Del (eq math.224637.5)

(force rerendering)

Occurrences on the following pages:

Hash: 2c7c77981be9b47e214e73ef7698ff2e

TeX (original user input):

\nabla = \left( {\partial \over \partial x}, {\partial \over \partial y}, {\partial \over \partial z} \right) = \mathbf{\hat{x}} {\partial \over \partial x} + \mathbf{\hat{y}} {\partial \over \partial y} + \mathbf{\hat{z}} {\partial \over \partial z}

TeX (checked):

\nabla =\left({\partial  \over \partial x},{\partial  \over \partial y},{\partial  \over \partial z}\right)=\mathbf {\hat {x}} {\partial  \over \partial x}+\mathbf {\hat {y}} {\partial  \over \partial y}+\mathbf {\hat {z}} {\partial  \over \partial z}

LaTeXML (experimental; uses MathML) rendering

MathML (10.958 KB / 1.518 KB) :

= ( x , y , z ) = 𝐱 ^ x + 𝐲 ^ y + 𝐳 ^ z 𝑥 𝑦 𝑧 ^ 𝐱 𝑥 ^ 𝐲 𝑦 ^ 𝐳 𝑧 {\displaystyle{\displaystyle\nabla=\left({\partial\over\partial x},{\partial% \over\partial y},{\partial\over\partial z}\right)=\mathbf{\hat{x}}{\partial% \over\partial x}+\mathbf{\hat{y}}{\partial\over\partial y}+\mathbf{\hat{z}}{% \partial\over\partial z}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\nabla=\left({\partial\over\partial x},{\partial%&#10;\over\partial y},{\partial\over\partial z}\right)=\mathbf{\hat{x}}{\partial%&#10;\over\partial x}+\mathbf{\hat{y}}{\partial\over\partial y}+\mathbf{\hat{z}}{%&#10;\partial\over\partial z}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">
      <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml"></mo>
      <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
      <mrow id="p1.1.m1.1.19.2" xref="p1.1.m1.1.19.2.1.cmml">
        <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.19.2.1.cmml">(</mo>
        <mstyle displaystyle="true" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
          <mfrac id="p1.1.m1.1.4a" xref="p1.1.m1.1.4.cmml">
            <mo id="p1.1.m1.1.4.2" xref="p1.1.m1.1.4.2.cmml"></mo>
            <mrow id="p1.1.m1.1.4.3" xref="p1.1.m1.1.4.3.cmml">
              <mo id="p1.1.m1.1.4.3.1" xref="p1.1.m1.1.4.3.1.cmml"></mo>
              <mo id="p1.1.m1.1.4.3a" xref="p1.1.m1.1.4.3.cmml"></mo>
              <mi id="p1.1.m1.1.4.3.2" xref="p1.1.m1.1.4.3.2.cmml">x</mi>
            </mrow>
          </mfrac>
        </mstyle>
        <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.19.2.1.cmml">,</mo>
        <mstyle displaystyle="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
          <mfrac id="p1.1.m1.1.6a" xref="p1.1.m1.1.6.cmml">
            <mo id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml"></mo>
            <mrow id="p1.1.m1.1.6.3" xref="p1.1.m1.1.6.3.cmml">
              <mo id="p1.1.m1.1.6.3.1" xref="p1.1.m1.1.6.3.1.cmml"></mo>
              <mo id="p1.1.m1.1.6.3a" xref="p1.1.m1.1.6.3.cmml"></mo>
              <mi id="p1.1.m1.1.6.3.2" xref="p1.1.m1.1.6.3.2.cmml">y</mi>
            </mrow>
          </mfrac>
        </mstyle>
        <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.19.2.1.cmml">,</mo>
        <mstyle displaystyle="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
          <mfrac id="p1.1.m1.1.8a" xref="p1.1.m1.1.8.cmml">
            <mo id="p1.1.m1.1.8.2" xref="p1.1.m1.1.8.2.cmml"></mo>
            <mrow id="p1.1.m1.1.8.3" xref="p1.1.m1.1.8.3.cmml">
              <mo id="p1.1.m1.1.8.3.1" xref="p1.1.m1.1.8.3.1.cmml"></mo>
              <mo id="p1.1.m1.1.8.3a" xref="p1.1.m1.1.8.3.cmml"></mo>
              <mi id="p1.1.m1.1.8.3.2" xref="p1.1.m1.1.8.3.2.cmml">z</mi>
            </mrow>
          </mfrac>
        </mstyle>
        <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.19.2.1.cmml">)</mo>
      </mrow>
      <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">=</mo>
      <mrow id="p1.1.m1.1.19.3" xref="p1.1.m1.1.19.3.cmml">
        <mrow id="p1.1.m1.1.19.3.1" xref="p1.1.m1.1.19.3.1.cmml">
          <mover accent="true" id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
            <mi id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.2.cmml">𝐱</mi>
            <mo stretchy="false" id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">^</mo>
          </mover>
          <mo id="p1.1.m1.1.19.3.1.1" xref="p1.1.m1.1.19.3.1.1.cmml"></mo>
          <mstyle displaystyle="true" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
            <mfrac id="p1.1.m1.1.12a" xref="p1.1.m1.1.12.cmml">
              <mo id="p1.1.m1.1.12.2" xref="p1.1.m1.1.12.2.cmml"></mo>
              <mrow id="p1.1.m1.1.12.3" xref="p1.1.m1.1.12.3.cmml">
                <mo id="p1.1.m1.1.12.3.1" xref="p1.1.m1.1.12.3.1.cmml"></mo>
                <mo id="p1.1.m1.1.12.3a" xref="p1.1.m1.1.12.3.cmml"></mo>
                <mi id="p1.1.m1.1.12.3.2" xref="p1.1.m1.1.12.3.2.cmml">x</mi>
              </mrow>
            </mfrac>
          </mstyle>
        </mrow>
        <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">+</mo>
        <mrow id="p1.1.m1.1.19.3.2" xref="p1.1.m1.1.19.3.2.cmml">
          <mover accent="true" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">
            <mi id="p1.1.m1.1.14.2" xref="p1.1.m1.1.14.2.cmml">𝐲</mi>
            <mo stretchy="false" id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">^</mo>
          </mover>
          <mo id="p1.1.m1.1.19.3.2.1" xref="p1.1.m1.1.19.3.2.1.cmml"></mo>
          <mstyle displaystyle="true" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
            <mfrac id="p1.1.m1.1.15a" xref="p1.1.m1.1.15.cmml">
              <mo id="p1.1.m1.1.15.2" xref="p1.1.m1.1.15.2.cmml"></mo>
              <mrow id="p1.1.m1.1.15.3" xref="p1.1.m1.1.15.3.cmml">
                <mo id="p1.1.m1.1.15.3.1" xref="p1.1.m1.1.15.3.1.cmml"></mo>
                <mo id="p1.1.m1.1.15.3a" xref="p1.1.m1.1.15.3.cmml"></mo>
                <mi id="p1.1.m1.1.15.3.2" xref="p1.1.m1.1.15.3.2.cmml">y</mi>
              </mrow>
            </mfrac>
          </mstyle>
        </mrow>
        <mo id="p1.1.m1.1.13a" xref="p1.1.m1.1.13.cmml">+</mo>
        <mrow id="p1.1.m1.1.19.3.3" xref="p1.1.m1.1.19.3.3.cmml">
          <mover accent="true" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">
            <mi id="p1.1.m1.1.17.2" xref="p1.1.m1.1.17.2.cmml">𝐳</mi>
            <mo stretchy="false" id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">^</mo>
          </mover>
          <mo id="p1.1.m1.1.19.3.3.1" xref="p1.1.m1.1.19.3.3.1.cmml"></mo>
          <mstyle displaystyle="true" id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
            <mfrac id="p1.1.m1.1.18a" xref="p1.1.m1.1.18.cmml">
              <mo id="p1.1.m1.1.18.2" xref="p1.1.m1.1.18.2.cmml"></mo>
              <mrow id="p1.1.m1.1.18.3" xref="p1.1.m1.1.18.3.cmml">
                <mo id="p1.1.m1.1.18.3.1" xref="p1.1.m1.1.18.3.1.cmml"></mo>
                <mo id="p1.1.m1.1.18.3a" xref="p1.1.m1.1.18.3.cmml"></mo>
                <mi id="p1.1.m1.1.18.3.2" xref="p1.1.m1.1.18.3.2.cmml">z</mi>
              </mrow>
            </mfrac>
          </mstyle>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">
        <and id="p1.1.m1.1.19a.cmml" xref="p1.1.m1.1.19"/>
        <apply id="p1.1.m1.1.19b.cmml" xref="p1.1.m1.1.19">
          <eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"></ci>
          <vector id="p1.1.m1.1.19.2.1.cmml" xref="p1.1.m1.1.19.2">
            <apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
              <divide id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4"/>
              <partialdiff id="p1.1.m1.1.4.2.cmml" xref="p1.1.m1.1.4.2"/>
              <apply id="p1.1.m1.1.4.3.cmml" xref="p1.1.m1.1.4.3">
                <partialdiff id="p1.1.m1.1.4.3.1.cmml" xref="p1.1.m1.1.4.3.1"/>
                <ci id="p1.1.m1.1.4.3.2.cmml" xref="p1.1.m1.1.4.3.2">𝑥</ci>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
              <divide id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6"/>
              <partialdiff id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2"/>
              <apply id="p1.1.m1.1.6.3.cmml" xref="p1.1.m1.1.6.3">
                <partialdiff id="p1.1.m1.1.6.3.1.cmml" xref="p1.1.m1.1.6.3.1"/>
                <ci id="p1.1.m1.1.6.3.2.cmml" xref="p1.1.m1.1.6.3.2">𝑦</ci>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
              <divide id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8"/>
              <partialdiff id="p1.1.m1.1.8.2.cmml" xref="p1.1.m1.1.8.2"/>
              <apply id="p1.1.m1.1.8.3.cmml" xref="p1.1.m1.1.8.3">
                <partialdiff id="p1.1.m1.1.8.3.1.cmml" xref="p1.1.m1.1.8.3.1"/>
                <ci id="p1.1.m1.1.8.3.2.cmml" xref="p1.1.m1.1.8.3.2">𝑧</ci>
              </apply>
            </apply>
          </vector>
        </apply>
        <apply id="p1.1.m1.1.19c.cmml" xref="p1.1.m1.1.19">
          <eq id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"/>
          <share href="#p1.1.m1.1.19.2.cmml" id="p1.1.m1.1.19d.cmml" xref="p1.1.m1.1.19"/>
          <apply id="p1.1.m1.1.19.3.cmml" xref="p1.1.m1.1.19.3">
            <plus id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
            <apply id="p1.1.m1.1.19.3.1.cmml" xref="p1.1.m1.1.19.3.1">
              <times id="p1.1.m1.1.19.3.1.1.cmml" xref="p1.1.m1.1.19.3.1.1"/>
              <apply id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
                <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">^</ci>
                <ci id="p1.1.m1.1.11.2.cmml" xref="p1.1.m1.1.11.2">𝐱</ci>
              </apply>
              <apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
                <divide id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12"/>
                <partialdiff id="p1.1.m1.1.12.2.cmml" xref="p1.1.m1.1.12.2"/>
                <apply id="p1.1.m1.1.12.3.cmml" xref="p1.1.m1.1.12.3">
                  <partialdiff id="p1.1.m1.1.12.3.1.cmml" xref="p1.1.m1.1.12.3.1"/>
                  <ci id="p1.1.m1.1.12.3.2.cmml" xref="p1.1.m1.1.12.3.2">𝑥</ci>
                </apply>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.19.3.2.cmml" xref="p1.1.m1.1.19.3.2">
              <times id="p1.1.m1.1.19.3.2.1.cmml" xref="p1.1.m1.1.19.3.2.1"/>
              <apply id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">
                <ci id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">^</ci>
                <ci id="p1.1.m1.1.14.2.cmml" xref="p1.1.m1.1.14.2">𝐲</ci>
              </apply>
              <apply id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">
                <divide id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15"/>
                <partialdiff id="p1.1.m1.1.15.2.cmml" xref="p1.1.m1.1.15.2"/>
                <apply id="p1.1.m1.1.15.3.cmml" xref="p1.1.m1.1.15.3">
                  <partialdiff id="p1.1.m1.1.15.3.1.cmml" xref="p1.1.m1.1.15.3.1"/>
                  <ci id="p1.1.m1.1.15.3.2.cmml" xref="p1.1.m1.1.15.3.2">𝑦</ci>
                </apply>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.19.3.3.cmml" xref="p1.1.m1.1.19.3.3">
              <times id="p1.1.m1.1.19.3.3.1.cmml" xref="p1.1.m1.1.19.3.3.1"/>
              <apply id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">
                <ci id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">^</ci>
                <ci id="p1.1.m1.1.17.2.cmml" xref="p1.1.m1.1.17.2">𝐳</ci>
              </apply>
              <apply id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
                <divide id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18"/>
                <partialdiff id="p1.1.m1.1.18.2.cmml" xref="p1.1.m1.1.18.2"/>
                <apply id="p1.1.m1.1.18.3.cmml" xref="p1.1.m1.1.18.3">
                  <partialdiff id="p1.1.m1.1.18.3.1.cmml" xref="p1.1.m1.1.18.3.1"/>
                  <ci id="p1.1.m1.1.18.3.2.cmml" xref="p1.1.m1.1.18.3.2">𝑧</ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\nabla=\left({\partial\over\partial x},{\partial%
\over\partial y},{\partial\over\partial z}\right)=\mathbf{\hat{x}}{\partial%
\over\partial x}+\mathbf{\hat{y}}{\partial\over\partial y}+\mathbf{\hat{z}}{%
\partial\over\partial z}}}</annotation>
  </semantics>
</math>

SVG (14.054 KB / 4.118 KB) :

nabla equals left-parenthesis StartFraction partial-differential Over partial-differential x EndFraction comma StartFraction partial-differential Over partial-differential y EndFraction comma StartFraction partial-differential Over partial-differential z EndFraction right-parenthesis equals ModifyingAbove bold x With caret times StartFraction partial-differential Over partial-differential x EndFraction plus ModifyingAbove bold y With caret times StartFraction partial-differential Over partial-differential y EndFraction plus ModifyingAbove bold z With caret times StartFraction partial-differential Over partial-differential z EndFraction

SVG (MathML can be enabled via browser plugin) rendering

MathML (3.664 KB / 548 B) :

= ( x , y , z ) = x ^ x + y ^ y + z ^ z {\displaystyle \nabla =\left({\partial \over \partial x},{\partial \over \partial y},{\partial \over \partial z}\right)=\mathbf {\hat {x}} {\partial \over \partial x}+\mathbf {\hat {y}} {\partial \over \partial y}+\mathbf {\hat {z}} {\partial \over \partial z}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \nabla =\left({\partial  \over \partial x},{\partial  \over \partial y},{\partial  \over \partial z}\right)=\mathbf {\hat {x}} {\partial  \over \partial x}+\mathbf {\hat {y}} {\partial  \over \partial y}+\mathbf {\hat {z}} {\partial  \over \partial z}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi mathvariant="normal">&#x2207;<!-- ∇ --></mi>
        <mo>=</mo>
        <mrow>
          <mo>(</mo>
          <mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <mfrac>
                <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
                <mrow>
                  <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
                  <mi>x</mi>
                </mrow>
              </mfrac>
            </mrow>
            <mo>,</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mfrac>
                <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
                <mrow>
                  <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
                  <mi>y</mi>
                </mrow>
              </mfrac>
            </mrow>
            <mo>,</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <mfrac>
                <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
                <mrow>
                  <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
                  <mi>z</mi>
                </mrow>
              </mfrac>
            </mrow>
          </mrow>
          <mo>)</mo>
        </mrow>
        <mo>=</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi mathvariant="bold">x</mi>
              <mo mathvariant="bold" stretchy="false">&#x005E;<!-- ^ --></mo>
            </mover>
          </mrow>
        </mrow>
        <mrow class="MJX-TeXAtom-ORD">
          <mfrac>
            <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
            <mrow>
              <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
              <mi>x</mi>
            </mrow>
          </mfrac>
        </mrow>
        <mo>+</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi mathvariant="bold">y</mi>
              <mo mathvariant="bold" stretchy="false">&#x005E;<!-- ^ --></mo>
            </mover>
          </mrow>
        </mrow>
        <mrow class="MJX-TeXAtom-ORD">
          <mfrac>
            <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
            <mrow>
              <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
              <mi>y</mi>
            </mrow>
          </mfrac>
        </mrow>
        <mo>+</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi mathvariant="bold">z</mi>
              <mo mathvariant="bold" stretchy="false">&#x005E;<!-- ^ --></mo>
            </mover>
          </mrow>
        </mrow>
        <mrow class="MJX-TeXAtom-ORD">
          <mfrac>
            <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
            <mrow>
              <mi mathvariant="normal">&#x2202;<!-- ∂ --></mi>
              <mi>z</mi>
            </mrow>
          </mfrac>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \nabla =\left({\partial  \over \partial x},{\partial  \over \partial y},{\partial  \over \partial z}\right)=\mathbf {\hat {x}} {\partial  \over \partial x}+\mathbf {\hat {y}} {\partial  \over \partial y}+\mathbf {\hat {z}} {\partial  \over \partial z}}</annotation>
  </semantics>
</math>

SVG (10.08 KB / 3.609 KB) :

{\displaystyle \nabla =\left({\partial \over \partial x},{\partial \over \partial y},{\partial \over \partial z}\right)=\mathbf {\hat {x}} {\partial \over \partial x}+\mathbf {\hat {y}} {\partial \over \partial y}+\mathbf {\hat {z}} {\partial \over \partial z}}

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Del page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results