Template:D/doc

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The {{d}} (differential) mathematical formatting template gives a standardized notation (e.g. italic 

d

(current choice) or roman 

d

for ordinary differentials) for differentials, in either HTML+CSS or LaTeX.

Usage

{{d|variable}}

or

{{d|variable|type}}

or

{{d|variable|format}}

or

{{d|variable|type|format}}

where the second argument, type, is either

• ord: to get an ordinary differential (default);
• ord:n: to get an ordinary 

  n

  th differential;
• part or partial: to get a partial differential;
• part:n or partial:n: to get a partial 

  n

  th differential;

and where the last argument, format, is either

• htm: to get HTML+CSS (default);
• tex: to get LaTeX.

Examples

Integrals

The code

where {{math|{{int|0|infty|''e''{{^|{{op|-}}''x''}} {{d|''x''}}}} {{=}} 1|&}}, and (...)

yields the text style HTML+CSS: where 

∫ ∞ 0  e  − x d x = 1

, and (...)

The code

where {{math|{{int|0|infty|''e''{{^|{{op|-}}''x''|tex}} {{d|''x''|tex}}|tex}} {{=}} 1|$}}, and (...)

yields the text style LaTeX: where$\textstyle {\int _{0}^{\infty }\;{e^{{\,}-{\,}x}d^{}x}=1}$, and (...)

Derivatives

The code

where {{math|{{vec|j|bold}}{{sp|1}}(''t'') {{=}} {{frac|{{d|{{vec|r|bold}}|ord:3}}|{{d|''t''{{^|3}}}}}}|&}}, and (...)

yields the text style HTML+CSS: where 

j (t) = d  3  r d t 3

, and (...)

The code

where {{math|{{vec|j|bold|tex}}(''t'') {{=}} {{frac|{{d|{{vec|r|bold|tex}}|ord:3|tex}}|{{d|''t''{{^|3|tex}}|tex}}|tex}}|$}}, and (...)

yields the text style LaTeX: where$\textstyle {\mathbf {j} (t)={\frac {d^{3}\mathbf {r} }{d^{}t^{3}}}}$, and (...)

The code

:{{math|{{vec|j|bold}}{{sp|1}}(''t'') {{=}} {{frac|{{d|{{vec|r|bold}}|ord:3}}|{{d|''t''{{^|3}}}}}}|&&}}

yields the display style HTML+CSS:

j (t) = d  3  r d t 3

The code

:{{math|{{vec|j|bold|tex}}(''t'') {{=}} {{frac|{{d|{{vec|r|bold|tex}}|ord:3|tex}}|{{d|''t''{{^|3|tex}}|tex}}|tex}}|$$}}

yields the display style LaTeX:

${\begin{array}{l}\displaystyle {\mathbf {j} (t)={\frac {d^{3}\mathbf {r} }{d^{}t^{3}}}}\end{array}}$

Partial differential equations

The code

{{math|
{{frac|{{d|''{{Gr|psi}}''|part:2}}|{{d|''x''{{^|2}}|part}}}} + {{frac|{{d|''{{Gr|psi}}''|part:2}}|{{d|''y''{{^|2}}|part}}}} + {{frac|{{d|''{{Gr|psi}}''|part:2}}|{{d|''z''{{^|2}}|part}}}} {{=}} <!--
-->{{frac|1|''v''{{^|2}}}} {{frac|{{d|''{{Gr|psi}}''|part:2}}|{{d|''t''{{^|2}}|part}}}} 
|&}}

yields the text style HTML+CSS: 

∂ 2  ψ ∂ x 2 + ∂ 2  ψ ∂ y 2 + ∂ 2  ψ ∂ z 2 = 1 v 2 ∂ 2  ψ ∂ t 2

The code

{{math|
{{frac|{{d|''{{Gr|psi|tex}}''|part:2|tex}}|{{d|''x''{{^|2|tex}}|part|tex}}|tex}} + {{frac|{{d|''{{Gr|psi|tex}}''|part:2|tex}}|{{d|''y''{{^|2|tex}}|part|tex}}|tex}} + {{frac|{{d|''{{Gr|psi|tex}}''|part:2|tex}}|{{d|''z''{{^|2|tex}}|part|tex}}|tex}} {{=}} <!--
-->{{frac|1|''v''{{^|2|tex}}|tex}} {{frac|{{d|''{{Gr|psi|tex}}''|part:2|tex}}|{{d|''t''{{^|2|tex}}|part|tex}}|tex}}
|$}}

yields the text style LaTeX:$\textstyle {{\frac {\,{\partial }^{2}\psi }{\,{\partial }^{}x^{2}}}+{\frac {\,{\partial }^{2}\psi }{\,{\partial }^{}y^{2}}}+{\frac {\,{\partial }^{2}\psi }{\,{\partial }^{}z^{2}}}={\frac {1}{v^{2}}}{\frac {\,{\partial }^{2}\psi }{\,{\partial }^{}t^{2}}}}$

The code

:{{math|
{{frac|{{d|''{{Gr|psi}}''|part:2}}|{{d|''x''{{^|2}}|part}}}} + {{frac|{{d|''{{Gr|psi}}''|part:2}}|{{d|''y''{{^|2}}|part}}}} + {{frac|{{d|''{{Gr|psi}}''|part:2}}|{{d|''z''{{^|2}}|part}}}} {{=}} <!--
-->{{frac|1|''v''{{^|2}}}} {{frac|{{d|''{{Gr|psi}}''|part:2}}|{{d|''t''{{^|2}}|part}}}} 
|&&}}

yields the display style HTML+CSS:

∂ 2  ψ ∂ x 2 + ∂ 2  ψ ∂ y 2 + ∂ 2  ψ ∂ z 2 = 1 v 2 ∂ 2  ψ ∂ t 2

The code

:{{math|
{{frac|{{d|''{{Gr|psi|tex}}''|part:2|tex}}|{{d|''x''{{^|2|tex}}|part|tex}}|tex}} + {{frac|{{d|''{{Gr|psi|tex}}''|part:2|tex}}|{{d|''y''{{^|2|tex}}|part|tex}}|tex}} + {{frac|{{d|''{{Gr|psi|tex}}''|part:2|tex}}|{{d|''z''{{^|2|tex}}|part|tex}}|tex}} {{=}} <!--
-->{{frac|1|''v''{{^|2|tex}}|tex}} {{frac|{{d|''{{Gr|psi|tex}}''|part:2|tex}}|{{d|''t''{{^|2|tex}}|part|tex}}|tex}}
|$$}}

yields the display style LaTeX:

${\begin{array}{l}\displaystyle {{\frac {\,{\partial }^{2}\psi }{\,{\partial }^{}x^{2}}}+{\frac {\,{\partial }^{2}\psi }{\,{\partial }^{}y^{2}}}+{\frac {\,{\partial }^{2}\psi }{\,{\partial }^{}z^{2}}}={\frac {1}{v^{2}}}{\frac {\,{\partial }^{2}\psi }{\,{\partial }^{}t^{2}}}}\end{array}}$

See also

• {{partial}} (to typeset partial derivative expressions)