以下のコマンドは、すべて数式を記述する環境の中で実行する。つまり、\begin{equation} - \end{equation}、または$ - $の中に記述する。
四則演算
1 + 2 - 3 \times 4 \div 5
a \times b \pm c \mp d
1 + 2 − 3 × 4 ÷ 5 1 + 2 - 3 \times 4 \div 5 1 + 2 − 3 × 4 ÷ 5 a × b ± c ∓ d a \times b \pm c \mp d a × b ± c ∓ d 指数・添え字
a^ 2 + b^ 2 = c^ 2
a_ {n + 1} = ca_ n + f(n)
a 2 + b 2 = c 2 a^2 + b^2 = c^2 a 2 + b 2 = c 2 a n + 1 = c a n + f ( n ) a_{n + 1} = ca_n + f(n) a n + 1 = c a n + f ( n ) 2文字以上を指定するときは{ }で囲む
三角関数
\tan {x} = \frac {\sin {x}}{\cos {x}}
\arccos {x} = \arcsin {\sqrt {1 - x^ 2}}
tan x = sin x cos x \tan{x} = \frac{\sin{x}}{\cos{x}} tan x = cos x sin x arccos x = arcsin 1 − x 2 \arccos{x} = \arcsin{\sqrt{1 - x^2}} arccos x = arcsin 1 − x 2 指数関数・対数関数
y = a^ x
\log _ {a}b^ x = x\log _ {a}{b}
\ln {e} = 1
log a b x = x log a b \log_{a}b^x = x\log_{a}{b} log a b x = x log a b 対数関数で底を明示するときは\log_{底}{真数}、底がいらないときは\log{真数}
分数
y = \frac {1}{x}
y = \cfrac {1}{a_ 0 + \cfrac {1}{a_ 1 + \cfrac {1}{a_ 2 + \cdots }}}
y = 1 a 0 + 1 a 1 + 1 a 2 + ⋯ y = \cfrac{1}{a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cdots}}} y = a 0 + a 1 + a 2 + ⋯ 1 1 1 微分・積分
(x^ 2 + 2x + 1)' = 2x + 2
\frac {\mathrm {d}}{\mathrm {d}x} \log {x} = \frac {1}{x}
\frac {\mathrm {d}^ 2}{\mathrm {d}x^ 2} x^ 2 = 2
\frac {\partial }{\partial x} (x^ 2 + xy) = 2x + y
\int x \mathrm {d}x = \frac {1}{2} x^ 2 + C
\int _ {b}^ {a} x \mathrm {d}x = \frac {1}{2} ( a^ 2 - b^ 2 )
( x 2 + 2 x + 1 ) ′ = 2 x + 2 (x^2 + 2x + 1)' = 2x + 2 ( x 2 + 2 x + 1 ) ′ = 2 x + 2 d d x log x = 1 x \frac{\mathrm{d}}{\mathrm{d}x} \log{x} = \frac{1}{x} d x d log x = x 1 d 2 d x 2 x 2 = 2 \frac{\mathrm{d}^2}{\mathrm{d}x^2} x^2 = 2 d x 2 d 2 x 2 = 2 ∂ ∂ x ( x 2 + x y ) = 2 x + y \frac{\partial}{\partial x} (x^2 + xy) = 2x + y ∂ x ∂ ( x 2 + x y ) = 2 x + y ∫ x d x = 1 2 x 2 + C \int x \mathrm{d}x = \frac{1}{2} x^2 + C ∫ x d x = 2 1 x 2 + C ∫ b a x d x = 1 2 ( a 2 − b 2 ) \int_{b}^{a} x \mathrm{d}x = \frac{1}{2} ( a^2 - b^2 ) ∫ b a x d x = 2 1 ( a 2 − b 2 ) 数列・極限
\sum _ {k = 1}^ {n} k = \frac {1}{2} n(n + 1)
\lim _ {x \to \infty } \frac {1}{x} = 0
∑ k = 1 n k = 1 2 n ( n + 1 ) \sum_{k = 1}^{n} k = \frac{1}{2} n(n + 1) k = 1 ∑ n k = 2 1 n ( n + 1 ) lim x → ∞ 1 x = 0 \lim_{x \to \infty} \frac{1}{x} = 0 x → ∞ lim x 1 = 0 二項係数
{}_ n \mathrm {C}_ r = \binom {n}{r}
n C r = ( n r ) {}_n \mathrm{C}_r = \binom{n}{r} n C r = ( r n ) ベクトル・行列
m \vec {a} = \vec {F}
\boldsymbol {a} = (a_ 1 \; a_ 2 \; a_ 3 \; \dots )
\| \boldsymbol {x} \|
\begin {bmatrix}
a & b \\
c & d \\
\end {bmatrix}
\begin {pmatrix}
a & b \\
c & d \\
\end {pmatrix}
\begin {vmatrix}
a & b \\
c & d \\
\end {vmatrix}
\begin {Vmatrix}
a & b \\
c & d \\
\end {Vmatrix}
a = ( a 1 a 2 a 3 … ) \boldsymbol{a} = (a_1 \; a_2 \; a_3 \; \dots) a = ( a 1 a 2 a 3 … ) m a ⃗ = F ⃗ m \vec{a} = \vec{F} m a = F ∥ x ∥ \| \boldsymbol{x} \| ∥ x ∥ [ a b c d ] \begin{bmatrix}
a & b \\
c & d \\
\end{bmatrix} [ a c b d ] ( a b c d ) \begin{pmatrix}
a & b \\
c & d \\
\end{pmatrix} ( a c b d ) ∣ a b c d ∣ \begin{vmatrix}
a & b \\
c & d \\
\end{vmatrix} a c b d ∥ a b c d ∥ \begin{Vmatrix}
a & b \\
c & d \\
\end{Vmatrix} a c b d