Patrocinado por PHPDocX

Síguenos en Twitter

Buscar en WikilleratO
   

Ayuda:Fórmulas Matemáticas

De Wikillerato

Ayuda

A continuación ofrecemos un cuadro de referencia con nociones básicas y ejemplos que sirven de ayuda para escribir fórmulas utilizando el código LaTeX.

Acentos
\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a} \acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}
\check{a} \bar{a} \ddot{a} \dot{a}  \check{a} \bar{a} \ddot{a} \dot{a}
Funciones estándar
\sin a \cos b \tan c  \sin a \cos b \tan c
\sec d \csc e \cot f  \sec d \csc e \cot f
\arcsin h \arccos i \arctan j  \arcsin h \arccos i \arctan j
\sinh k \cosh l \tanh m \coth n  \sinh k \cosh l \tanh m \coth n
\lim u \limsup v \liminf w \min x \max y  \lim u \limsup v \liminf w \min x \max y
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g  \inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g
Derivadas
\nabla \partial x dx \dot x \ddot y  \nabla \partial x dx \dot x \ddot y
Conjuntos
\forall \exists \emptyset \varnothing  \forall \exists \emptyset \varnothing
\in \ni \notin \subset \subseteq \supset \supseteq  \in \ni \notin \subset \subseteq \supset \supseteq
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus  \cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup  \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup
Operadores
+ \oplus \bigoplus \pm \mp -  + \oplus \bigoplus \pm \mp -
\times \otimes \bigotimes \cdot \circ \bullet \bigodot  \times \otimes \bigotimes \cdot \circ \bullet \bigodot
\star * / \div \frac{1}{2}  \star * / \div \frac{1}{2}
Lógica
\land \wedge \bigwedge \bar{q} \to p  \land \wedge \bigwedge \bar{q} \to p
\lor \vee \bigvee \lnot \neg q \And  \lor \vee \bigvee \lnot \neg q \And
Raíces
\sqrt{2} \sqrt[n]{x}  \sqrt{2} \sqrt[n]{x}
Relaciones
\sim \approx \simeq \cong  \sim \approx \simeq \cong
\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto  \le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto
Geometría
\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ  \Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ
Flechas
\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow  \leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow
\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft  \uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft
\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow  \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow
\Longrightarrow \Uparrow \Downarrow \Updownarrow  \Longrightarrow \Uparrow \Downarrow \Updownarrow
\nLeftrightarrow \longleftrightarrow  \nLeftrightarrow \longleftrightarrow
Especial
\eth \S \P \% \dagger \ddagger \ldots \cdots  \eth \S \P \% \dagger \ddagger \ldots \cdots
\smile \frown \wr \triangleleft \triangleright \infty \bot \top  \smile \frown \wr \triangleleft \triangleright \infty \bot \top
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar  \vdash \vDash \Vdash \models \lVert \rVert \imath \hbar
Otros
\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown  \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown
\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge  \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge
\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes  \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes
\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant  \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant
\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot  \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot
\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox  \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox
\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot  \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot
\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq  \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq
\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork  \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork
\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq  \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq
\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid  \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid
\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \ngtr  \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \ngtr
\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq  \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq
\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq  \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq
\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq  \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq

Subíndices, superíndices, integrales

  Sintaxis Cómo se verá
HTML PNG
Superíndice a^2 a2  a^2
Subíndice a_2 >a2  a_2
Agrupar a^{2+2} a2 + 2  a^{2+2}
a_{i,j} ai,j  a_{i,j}
Combinar superíndice y subíndice x_2^3  x_2^3
Superíndices y subíndices, anteriores, posteriores, arriba y abajo \sideset{_1^2}{_3^4}\prod_a^b  \sideset{_1^2}{_3^4}\prod_a^b
{}_1^2\!\Omega_3^4  {}_1^2\!\Omega_3^4
Apilar \overset{\alpha}{\omega}  \overset{\alpha}{\omega}
\underset{\alpha}{\omega} [Unparseable or potentially dangerous latex formula. Error 3 ]
\overset{\alpha}{\underset{\gamma}{\omega}}  \overset{\alpha}{\underset{\gamma}{\omega}}
\stackrel{\alpha}{\omega}  \stackrel{\alpha}{\omega}
Derivadas ( forzando el PNG) x', y, f', f  x', y'', f', f''
Subrayado, línea superior, vectores \hat a \ \bar b \ \vec c  \hat a \ \bar b \ \vec c
\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}  \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}
\overline{g h i} \ \underline{j k l}  \overline{g h i} \ \underline{j k l}
Flechas A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C  A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
Llaves superiores \overbrace{ 1+2+\cdots+100 }^{5050}  \overbrace{ 1+2+\cdots+100 }^{5050}
Llaves inferiores \underbrace{ a+b+\cdots+z }_{26}  \underbrace{ a+b+\cdots+z }_{26}
Sumatorios \sum_{k=1}^N k^2  \sum_{k=1}^N k^2
Productorio \prod_{i=1}^N x_i  \prod_{i=1}^N x_i
Coproduct \coprod_{i=1}^N x_i  \coprod_{i=1}^N x_i
Límite \lim_{n \to \infty}x_n  \lim_{n \to \infty}x_n
Integral \int_{-N}^{N} e^x\, dx \int_{-N}^{N} e^x\, dx
Integral doble \iint_{D}^{W} \, dx\,dy  \iint_{D}^{W} \, dx\,dy
Integral triple \iiint_{E}^{V} \, dx\,dy\,dz  \iiint_{E}^{V} \, dx\,dy\,dz
Integral de línea \oint_{C} x^3\, dx + 4y^2\, dy  \oint_{C} x^3\, dx + 4y^2\, dy
Intersecciones \bigcap_1^{n} p  \bigcap_1^{n} p
Uniones \bigcup_1^{k} p  \bigcup_1^{k} p

actualizando

   
 
ASIGNATURAS
MatemáticasFísicaQuímicaBiologíaDibujoHistoriaLengua y LiteraturaHistoria del ArteFilosofía
Creative Commons License
Los contenidos de Wikillerato están disponibles bajo una licencia de Creative Commons.
Pueden utilizarse y redistribuirse libremente siempre que se reconozca su procedencia.