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ddrg
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math_formulas

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int64
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55.9k
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10,815
d/dx x^{\frac{1}{2}} + d/dx z^{\dfrac{1}{2}} = \frac{d}{dx} z^4 + d/dx x^4
10,296
L \cdot U \cdot y = c \Rightarrow y = \frac{c}{L \cdot U}
1,025
\overline{l + v} = \overline{l} + \overline{v}
2,700
7^1\cdot 3^0\cdot 2 \cdot 2\cdot 5^0 = 28
-19,417
\frac{9 \cdot 1/7}{1/9 \cdot 4} = 9/4 \cdot 9/7
29,642
z^{\frac{80}{5}} = z^{16}
21,626
\frac{z_3 - z_1}{-z_2 + z_3}\cdot \frac{z_2}{z_1} = \frac{\frac{z_3}{z_1} + (-1)}{(-1) + \tfrac{z_3}{z_2}}
21,275
(n + 1)! = n\cdot (1 + n)\cdot \cdots\cdot 2
-22,290
21 + z^2 - 10 z = (z + 3(-1)) (z + 7(-1))
-16,596
7*80^{1/2} = (16*5)^{1/2}*7
3,242
p i t q = 2 p i q t/2
-1,089
\frac{\left(-3\right) \dfrac{1}{8}}{(-1) \cdot 1/5} = -\frac51 (-3/8)
-1,798
-\frac{\pi}{3} = -\pi/3 + 0
32,421
(r e^{i \pi/4})^4 = r^4 \cdot (\cos\left(\frac{4 \pi}{4}\right) + i \sin(\frac{4 \pi}{4})) = -r^4
6,356
\dfrac12 - p = \frac{1}{\left(p - 1/2\right)^4} \Rightarrow \left(p - 1/2\right)^5 = -1
50,497
\infty^0= 1
-3,892
11 \times z/4 = z \times 11/4
16,995
1^{-1} + 1^{-1} + \frac{1}{2} = 2.5
-591
(e^{13 \cdot \pi \cdot i/12})^{10} = e^{\frac{13}{12} \cdot i \cdot \pi \cdot 10}
28,112
(\sqrt{5} + \sqrt{7}) - \sqrt{5} = \sqrt{7} \in L'
8,347
\frac{1}{y - b_k} (y - f_k) + \left(-1\right) = \frac{1}{y - b_k} (y - f_k - y + b_k) = \dfrac{b_k - f_k}{y - b_k}
8,348
(x + 1) \cdot (h + 1) + (-1) = h \cdot x + x + h
6,884
\sin(π + c) = -\sin(c)
48,333
{45 \choose 5} = {5 + 40 \choose 5}
-2,547
16^{1/2} \cdot 6^{1/2} + 4^{1/2} \cdot 6^{1/2} = 2 \cdot 6^{1/2} + 4 \cdot 6^{1/2}
13,882
-(-2)^{\left(-1\right) + n} \cdot 2 = (-2)^n
50,251
({7 \choose 2} {9 \choose 2} + {7 \choose 1} {8 \choose 1})*6! = 584640
-24,884
\frac{1}{18} \cdot 17 = s/6 \cdot 6 = s
-22,228
(y + 6) \cdot (y + 8) = y^2 + y \cdot 14 + 48
9,754
r^i\cdot s\cdot r^t = r^i\cdot s\cdot r^t
-1,618
\pi\cdot \frac{10}{3} = \frac{17}{12}\cdot \pi + \dfrac{23}{12}\cdot \pi
34,257
F \cdot F = F\cdot F^1 = F^1\cdot F
31,397
\frac{1}{z} \times z = \frac{z}{z} \times 1/z \times z = \left(\frac1z \times z\right)^2
4,898
\frac{1}{X\cdot E} = 1/(E\cdot X)
14,676
45\cdot \left(-1\right) + 25 = 36\cdot (-1) + 16
-3,431
-\sqrt{3} + \sqrt{3}\cdot 4 = \sqrt{3}\cdot \sqrt{16} - \sqrt{3}
-10,665
10 = -4 - 2*r + 10 = -2*r + 6
29,650
w + P + P + w = P + w + P + w
29,312
\frac{\cos(x)}{\sin\left(x\right)} = \cot(x)
2,866
\sin{q} = 0 = \sin{n \cdot \pi} \Rightarrow n \cdot \pi = q
48,139
2!\cdot {3 \choose 2}\cdot 2! = 2!\cdot \frac{3!}{2!\cdot 1!}\cdot 2! = 2!\cdot 3! = 2\cdot 6 = 12
11,388
2/49 = \frac17*2/7
16,317
\frac23 + \frac{7}{6} = \frac16 \cdot 11 = 5/3 + 1/6
3,752
\frac{3}{50} = \frac{3}{3 + 5} \cdot 0.4 \cdot \frac{8}{8 + 4} \cdot (1 - 0.4)
11,686
CE + EB = \left(C + B\right) E
-1,633
-0 \cdot \pi + \pi \cdot 13/12 = \pi \cdot 13/12
30,013
3(-1) + y^2 - 2y = (y + 1) (y + 3(-1))
13,661
0.09 = x + h \implies x \cdot 12.5 + 12.5 \cdot h
5,472
(-(b - \delta)^2 + (b + \delta)^2)/4 = \delta*b
-23,204
-3/2 \cdot 9 = -\frac12 \cdot 27
7,133
\frac{15 \cdot 13 \cdot 12 \cdot 14}{5 \cdot 4 \cdot 3 \cdot 2} \cdot 16 = \binom{16}{5}
30,736
\mathbb{Var}[T] = \mathbb{Var}[-T]
25,038
\frac{1}{g*x} = 1/(g*x)
-12,136
11/12 = \frac{1}{12\cdot \pi}\cdot q\cdot 12\cdot \pi = q
-20,347
(-40\times x + 16\times (-1))/(-80) = \dfrac{8}{8}\times \dfrac{1}{-10}\times (2\times (-1) - x\times 5)
42,699
\sqrt{42900} = \sqrt{429}\cdot 10
-26,628
k_2^2\cdot 25 + 9\cdot k_1^2 + k_2\cdot k_1\cdot 30 = (k_1\cdot 3 + 5\cdot k_2)^2
-16,602
7\cdot \sqrt{16}\cdot \sqrt{5} = 7\cdot 4\cdot \sqrt{5} = 28\cdot \sqrt{5}
7,070
\dfrac12*(a + b + f)*\left((-b + f)^2 + (-b + a)^2 + \left(-f + a\right)^2\right) = a^3 + b^3 + f^3 - 3*a*f*b
-6,087
\frac{4}{28 \cdot (-1) + 4 \cdot r} = \frac{4}{4 \cdot (r + 7 \cdot (-1))}
6,269
\frac12\cdot (\left(-1\right) + p)\cdot 2 = p + (-1)
29,354
h > -1\Longrightarrow 1 + h \gt 0
918
\tfrac{n}{-\frac{1}{2^n} + 1}*\tfrac{1}{2^n} = \frac{1}{2^n + (-1)}*n
-611
\frac{1}{12}\cdot 143\cdot \pi - 10\cdot \pi = 23/12\cdot \pi
19,761
\sqrt{n} = n^{1/3} \times n^{\frac16}
6,183
\frac{1}{G \cdot x} = \frac{1}{G \cdot x}
32,298
e_1 - e_2 = -(e_2 - e_1)
5,281
|z + \varepsilon + 2(-1)| = |z + (-1) + \varepsilon + \left(-1\right)| \leq |z + \left(-1\right)| + |\varepsilon + (-1)|
11,068
\dfrac12*(90 + 60*(-1)) = 15
36,482
2^3 \times 3! \times 3! = 288
13,277
|\frac{1}{x\cdot b_n}\cdot (-L\cdot b_n + a_n\cdot x)| = |-\frac{L}{x} + \frac{a_n}{b_n}|
25,144
-1 = (-1)^3 = (-1)^{\frac12 \cdot 6} = ((-1)^6)^{\frac{1}{2}} = 1
-7,926
\frac{20 - 21 \cdot i}{i \cdot 2 + 5} = \frac{-21 \cdot i + 20}{5 + 2 \cdot i} \cdot \dfrac{1}{-i \cdot 2 + 5} \cdot (-i \cdot 2 + 5)
22,337
\sin{z}*\cos{z} = \sin{z*2}/2
-11,902
3.984\cdot 0.1 = \frac{3.984}{10}
-3,055
(5 + 2 \cdot (-1)) \cdot 7^{1/2} = 7^{1/2} \cdot 3
19,596
\left\lfloor{\dfrac12*(100 + 3*\left(-1\right) + 1)}\right\rfloor = 49
27,601
1 + (-1) + 1 + \left(-1\right) + \dots = 1/2
33,947
3\pi/4 = \pi \frac{1}{4}3
-29,988
n\cdot I^{n + (-1)} = \frac{d}{dI} I^n
20,448
\frac{1}{20} \cdot 9 + 1/10 = 11/20
-4,715
\frac{1}{5 + z^2 + 6*z}*(15 + 7*z) = \frac{5}{z + 5} + \frac{1}{z + 1}*2
24,670
\frac{7 \cdot z^6}{-z + z^7} - \frac{(-1) + z^6 \cdot 7}{z^7 - z} = \frac{1}{z^7 - z}
5,774
\frac{1}{6} + 1/5 = \frac{1}{30}\cdot 11
-20,401
4/4\cdot \dfrac{1}{6\cdot \left(-1\right) + p}\cdot (3 - p\cdot 10) = \dfrac{12 - 40\cdot p}{4\cdot p + 24\cdot (-1)}
-26,020
\frac{1}{4 + i} \times \left(-7 \times i + 6\right) = \tfrac{-i \times 7 + 6}{4 + i} \times \tfrac{1}{4 - i} \times (4 - i)
8,604
\frac{1}{y + 1}\cdot \left(y^3 + y^2\cdot 4 + y + 2\cdot \left(-1\right)\right) = y \cdot y + y\cdot 3 + 2\cdot (-1)
21,954
\left|{H}\right| \coloneqq \left|{H}\right|
11,774
(c\cdot 0)^2 = c\cdot 0
30,049
t = \cos(\arccos\left(t\right))
21,459
\frac{(\frac{3}{5})^x + (\frac45)^x}{(2/5)^x + 1} = \frac{1}{2^x + 5^x}*(4^x + 3^x)
-13,928
5\cdot (4 + 7) = 5\cdot 11 = 55
28,060
11 = \frac13 + \frac43\cdot 8
43,673
768 = 8\cdot 3!\cdot 2^4
-23,084
2\left(-\frac{1}{3}2\right) = -4/3
33,931
2\sin\left(t\right) \cos(t) = \sin\left(2t\right)
-189
\dfrac{10!}{5! \cdot (10 + 5 \cdot \left(-1\right))!} = \binom{10}{5}
-18,270
\frac{5 \cdot g + g^2}{g^2 - g + 30 \cdot (-1)} = \frac{g \cdot \left(g + 5\right)}{(5 + g) \cdot \left(g + 6 \cdot (-1)\right)}
-11,523
-15 + 25 i = i\cdot 25 - 20 + 5
21,149
x^yx^z = x^{y + z}