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ddrg
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math_formulas

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39,126
s + s = (s + s) \cdot (s + s) = s^2 + s^2 + s^2 + s^2 = s + s + s + s
14,167
\frac{t}{e^{q \times t}} = e^{-t \times q} \times t
-29,594
\frac{\mathrm{d}}{\mathrm{d}x} (3 \cdot x^4) = 3 \cdot \frac{\mathrm{d}}{\mathrm{d}x} x^4 = 3 \cdot 4 \cdot x^3 = 12 \cdot x \cdot x \cdot x
3,257
y\cdot B^2 + 5\cdot y\cdot B + 4\cdot y = (4 + B^2 + 5\cdot B)\cdot y
-5,002
15.8 \cdot 10^2 = 10^{3 - 1} \cdot 15.8
3,697
(a + b)\cdot (-a + b) = b \cdot b - a^2
14,411
3 \leq x \Rightarrow e^{x + \left(-1\right)} > 2^{x + (-1)} \geq 2^{x + \left(-1\right)} = \left(1 + 1\right)^{x + (-1)}
37,091
\tfrac{1}{x}\cdot \xi = 1/\left(1/\xi\cdot x\right)
9,038
\frac{1}{x + 2 \cdot (-1)} \cdot \left(2 \cdot x^3 - 10 \cdot x + 4\right) = 2 \cdot x^2 + 4 \cdot x + 2 \cdot (-1)
-460
e^{2 \times \pi \times i} = e^{\pi \times i} \times e^{\pi \times i} = (-1)^2 = 1
8,335
\sin{2*y} = 2*\sin{y}*\cos{y} rightarrow \sin^{22}{y} = 4*\sin^2{y}*\cos^2{y}
11,877
S*W = I \Rightarrow W*S = I
-5,016
10^3 \cdot 0.84 = 0.84 \cdot 10^{2 - -1}
11,795
x*3 = \frac{\mathrm{d}}{\mathrm{d}x} (\frac12 + \frac32 x^2)
5,484
\tfrac{35}{12} = 91/6 - (\dfrac72)^2
-6,053
\frac{1}{27 (-1) + m^2 + m \cdot 6}4 = \frac{1}{(m + 9) (m + 3(-1))}4
-20,958
\dfrac{3 \cdot x}{x \cdot 3} \cdot (-\frac14 \cdot 7) = \dfrac{(-21) \cdot x}{12 \cdot x}
4,425
\cos{x \cdot f} = \cos(0.5 \cdot x \cdot f + 0.5 \cdot x \cdot f) = \cos^2{0.5 \cdot x \cdot f} - \sin^2{0.5 \cdot x \cdot f}
-3,509
\frac{3*5}{5*20} = 15/100
3,906
\frac{x}{(x^2 + a^2)^2} = \dfrac{x}{a^2 + x^2}\frac{1}{x^2 + a^2}
30,543
4\cdot π\cdot 2 = 8\cdot π
-4,528
\frac{-z + 7}{z^2 - 5z + 4} = \frac{1}{z + 4(-1)} - \dfrac{2}{(-1) + z}
9,110
x \cdot y + 12 \cdot (-1) = (x + 3 \cdot \left(-1\right) + 3) \cdot (y + 4 \cdot (-1) + 4) + 12 \cdot (-1) = \left(x + 3 \cdot (-1)\right) \cdot \left(y + 4 \cdot (-1)\right) + 4 \cdot (x + 3 \cdot (-1)) + 3 \cdot (y + 4 \cdot (-1))
17,372
1 + 2*x + 3*x^2 + \dotsm + x^{n + (-1)}*n = \dfrac{1}{(1 - x)^2}*(1 + n*x^{1 + n} - (n + 1)*x^n)
-22,428
125^{\frac13} = 5
12,865
\|-\theta + y\| = \sqrt{(y - \theta) \cdot (y - \theta)}
-472
\left(e^{\dfrac{\pi i}{12} 5}\right)^9 = e^{9 i \pi\cdot 5/12}
42,282
0.3 \times 4 = 1.2
-525
(e^{\frac{i}{6}\cdot \pi})^4 = e^{\frac{i\cdot \pi}{6}\cdot 4}
-5,210
10^{\left(-4\right)*(-1) + 1}*7.1 = 7.1*10^5
7,758
(-1) + 2y < 1 + y\Longrightarrow 2 > y
-3,757
96/120 \cdot \frac{1}{z^3} \cdot z^3 = \frac{96 \cdot z^3}{120 \cdot z^3}
21,546
\frac{n \cdot (k + 2 \cdot \left(-1\right))}{2 \cdot \left(-1\right) + n \cdot k} = \frac{1}{n \cdot k + 2 \cdot \left(-1\right)} \cdot (k \cdot n + 2 \cdot (-1) - (n + (-1)) \cdot 2)
16,278
(1 + x)^{\delta + 1} = \left(1 + x\right) (1 + x)^\delta \geq (1 + x) \left(1 + \delta x\right)
32,465
2\times \cos(x)\times \sin(x) = \sin\left(2\times x\right)
-4,427
\frac{-5 \cdot x + 8 \cdot (-1)}{x^2 + x \cdot 3 + 2} = -\frac{3}{1 + x} - \dfrac{2}{x + 2}
14,839
(2 + k * k + 3*k)/2 - \dfrac{1}{2}*(k + k^2) = 1 + k
700
a^{-z} = (e^{\ln\left(a\right)})^{-z} = e^{-z\cdot \ln\left(a\right)}
15,850
{v + (-1) + l + 2*(-1) \choose l + 2*\left(-1\right)} = {3*(-1) + v + l \choose l + 2*(-1)}
4,212
2\cdot (3\cdot (-1) + 6\cdot 8) = 90
8,419
\cosh(2*x) = \cosh^2(x) + \sinh^2\left(x\right) = 1 + 2*\sinh^2(x)
32,126
2*s - s^2 + s - 2*s^2 + s^3 = s*3 - 3*s^2 + s^3
20,469
5/7 = \dfrac{2 + 3}{5 + 2}
19,612
|\dfrac{A}{E}| = |A|/|E|
16,704
27*\left(1 + \frac13 + 0.12/27\right) = 36.12
18,331
\operatorname{asin}(-1/2) = (\pi*(-1))/6
25,725
(x + \left(-1\right))*(5*(-1) + 3*x^3 - x^2*5 - x*5) = 3*x^4 - 8*x^2 * x + 5
3,041
\dfrac{l}{l + 1} = 1 - \frac{1}{1 + l}
31,420
A - A - B = A \cap A \cap B^\complement^\complement = A \cap \left(B \cup A^\complement\right) = A \cap B
22,875
x^3 + x*3 + 4\left(-1\right) = \left(x + (-1)\right) (x * x + x + 4)
16,887
\cos{\theta_2} \sin{\theta_1} + \cos{\theta_1} \sin{\theta_2} = \sin\left(\theta_2 + \theta_1\right)
-6,128
\frac{1}{x^2 - 14 \cdot x + 45} \cdot 3 = \frac{1}{(x + 9 \cdot \left(-1\right)) \cdot (x + 5 \cdot (-1))} \cdot 3
1,263
\cos(2 \cdot Z) = 1 - 2 \cdot \sin^2(Z) = 2 \cdot \cos^2(Z) + \left(-1\right)
-4,284
\frac{1}{z^2}z^2 * z = zz z/(zz) = z
34,522
\int \sin^2{z}\,dz = \int \sin{z}*\sin{z}\,dz
2,011
\dfrac{1}{2 z^2 + y z - y^2} (-y^2 + z^2*2 - y z) = 1 - \frac{2 z y}{-y^2 + 2 z^2 + y z}
22,844
x^2 - r^2 = (r + x) \cdot (x - r)
35,619
\frac{1}{12321} + 12319/24642 = \tfrac{1}{2}
-20,459
\frac{n*2 + 5*(-1)}{n*2 + 5*(-1)}*(-\dfrac71) = \tfrac{35 - 14*n}{n*2 + 5*(-1)}
12,253
\frac{1}{3}\cdot 2\cdot 1/3\cdot \frac23 = \tfrac{4}{27}
-5,282
10^{3 + (-1)} \cdot 0.97 = 0.97 \cdot 10 \cdot 10
807
1 - -\sin\left(x\right) + 1 = \sin(x)
-6,429
\tfrac{2}{2\cdot (r + 8\cdot (-1))} = \frac{2}{16\cdot (-1) + r\cdot 2}
21,948
a*2 = 17 \Rightarrow \frac{17}{2} = a
19,409
|y^l| = \left(1 + |y| + (-1)\right)^l \gt 1 + (|y| + (-1))\times l
-2,661
3^{\dfrac{1}{2}} = (3(-1) + 4) \cdot 3^{\frac{1}{2}}
10,611
\frac{\mathrm{d}}{\mathrm{d}x} \sin(x \cdot x) = x \cdot \cos(x^2) \cdot 2
19,439
1 = z\cdot m + y\cdot n\Longrightarrow z\cdot m = -n\cdot y + 1
1,250
3*2!/36 = 6/36 = \frac{1}{6}
24,916
-y \cdot 8 + x^2 + y^2 - 6 \cdot x = 0 \implies (x + 3 \cdot (-1))^2 + (4 \cdot (-1) + y)^2 = 5^2
33,851
(2^7 + 2(-1))/7 = 18
17,602
-V/2 + V = \dfrac{V}{2}
16,623
\frac37\cdot \frac26/5 = 1/35
35,314
\frac{1}{4}\times \left(1 + 51\right) = 13
3,488
4*(-1) + 67 = 63
-1,244
-6/1 \cdot (-2/5) = \tfrac{\left(-2\right) \cdot \frac15}{\frac{1}{6} \cdot (-1)}
-29,169
0\cdot (-1) = 0
-11,642
2*i - 6 = 0 + 6*\left(-1\right) + i*2
6,998
15 \leq n \Rightarrow n \geq 1 + \frac{14}{15} \cdot n
-4,651
-\frac{1}{z + 5(-1)} + \frac{1}{z + 2\left(-1\right)}4 = \tfrac{1}{10 + z^2 - z\cdot 7}(18 (-1) + z\cdot 3)
12,755
(1 + n^2) \cdot (n \cdot n + (-1)) = n^4 + \left(-1\right)
18,591
(X + 3)^2 = X^2 + 6\cdot X + 9 = X^2 + 5\cdot X + 7 + X + 2
-1,091
-9/30 = \dfrac{(-9)*1/3}{30*1/3} = -3/10
2,379
2 \cdot (-1) + 2 \cdot \left(x + 1\right) + 5 \cdot x = 7 \cdot x
301
(h^2 + c^2 + c\cdot h)\cdot \left(-h + c\right) = -h^3 + c^3
-20,414
\frac{1}{24\cdot (-1) + p\cdot 4}\cdot (42\cdot (-1) + p\cdot 7) = 7/4\cdot \frac{6\cdot \left(-1\right) + p}{p + 6\cdot (-1)}
19,235
|-T + S| = |-S + T|
4,801
r^4 + 1 = (r^2 + (-1))^2 + 2r \cdot r = (r^2 + (-1))^2 - r \cdot r = (r^2 - r + (-1)) (r^2 + r + \left(-1\right))
-29,321
7i - 6 + 2 = 7i - 4
1,498
7^2 + (-2)^2 = 49 + 4 = 53 = r^2 \implies \sqrt{53} = r
285
\sin{2a} = \cos{a} \sin{a} \cdot 2
-12,771
15 = 4*(-1) + 19
33,617
U\cdot Y\cdot |X| = Y\cdot |X|\cdot U
8,450
a_n^3-a^3=(a_n-a)(a_n^2+aa_n+a^2)
3,974
S \coloneqq S_1 S_2 \dotsm S_l \coloneqq S_1 S_2 \dotsm S_l
1,972
a \cdot \zeta = a \cdot \zeta
23,197
G^r\cdot G^x = G^{x + r}
-3,664
\frac{9}{5 \times l^2} = \frac{9}{l^2} \times \dfrac15
14,746
2 \cdot m^2 + 6 = m \cdot m + m^2 + 6 \geq m^2 + 2 \cdot m + 6 = \left(m + 1\right)^2 + 5 > (m + 1)^2 + 3
1,256
h_1^3\cdot h_1^3\cdot h_2 = h_1^6\cdot h_2 = h_1 \cdot h_1\cdot h_2