instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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Let q(y) = 165*y + 23. Let s(a) = 1495*a + 210. Let d(g) = 35*q(g) - 4*s(g). Let i(l) = -34*l - 6. Give 6*d(x) - 35*i(x).\n | -40*x\n | ibivibiv/math_instruct | |
Solve 0 = 2*t + 1515*o - 1516*o - 18, -5*o - 6 = 2*t for t.\n | 7\n | ibivibiv/math_instruct | |
Express -2*d**2 + 7*d**2 - d**2 + (4*d - 2*d - 3*d)*(8*d + 0*d - 3*d) in the form t + n*d + r*d**2 and give r.\n | -1\n | ibivibiv/math_instruct | |
In base 8, what is -24206 + -3?\n | -24211\n | ibivibiv/math_instruct | |
Express (-4*m + 2*m + m)*(-3*m + m + 17 - 7) as i + q*m**2 + v*m and give q.\n | 2\n | ibivibiv/math_instruct | |
Round 95569.2 to the nearest 10000.\n | 100000\n | ibivibiv/math_instruct | |
Express 4*d**2 + 40*d**3 + 3 - 5*d**2 - 2*d**4 - 64*d**3 - d - 32*d**3 as t*d**4 + b*d**2 + w*d + p + m*d**3 and give w.\n | -1\n | ibivibiv/math_instruct | |
Simplify -5*-6*4*(-3 + (sqrt(171) - (sqrt(171) + -6*(sqrt(171) + -2 + sqrt(171)))**2))*3.\n | -7501680 + 286200*sqrt(19)\n | ibivibiv/math_instruct | |
Solve -10/7*j**2 - 4/7*j**5 + 4/7 + 6/7*j**4 + 10/7*j**3 - 6/7*j = 0.\n | -1, 1/2, 1, 2\n | ibivibiv/math_instruct | |
Expand (t + 0*t - 3*t)*(3*t - 2*t - 4*t) + 2 + 6 + 328*t**2 + 28*t**2 - 8.\n | 362*t**2\n | ibivibiv/math_instruct | |
Simplify -4 + sqrt(10)/sqrt(2) + -2 + (sqrt(5) - (sqrt(5) + -1)) + 0.\n | -5 + sqrt(5)\n | ibivibiv/math_instruct | |
Sort -4, 63, 2, 7, 5 in descending order.\n | 63, 7, 5, 2, -4\n | ibivibiv/math_instruct | |
Put 6, 0.5, 1, 3, 105 in increasing order.\n | 0.5, 1, 3, 6, 105\n | ibivibiv/math_instruct | |
Let t(q) = -7*q - 15. What is t(4)?\n | -43\n | ibivibiv/math_instruct | |
Calculate the common denominator of -1/4246660 and 94/15.\n | 12739980\n | ibivibiv/math_instruct | |
Solve 6803 = -845*p + 123*p - 4027 for p.\n | -15\n | ibivibiv/math_instruct | |
Let m be ((-2)/(-6))/((-1)/(-21)). Let t = 3 + m. What are the prime factors of t?\n | 2, 5\n | ibivibiv/math_instruct | |
Suppose -u - 3*u = -196. What is the tens digit of u?\n | 4\n | ibivibiv/math_instruct | |
In base 12, what is -3 + 9056?\n | 9053\n | ibivibiv/math_instruct | |
Let o = 191 + -187. Which is the third biggest value? (a) 3 (b) o (c) 6 (d) -6\n | a\n | ibivibiv/math_instruct | |
Suppose -6*t + 4*x = -2*t + 40, 3*t - 5*x = -40. Let f(l) be the second derivative of -2*l**3 + 2*l**2 - 23*l. What is the tens digit of f(t)?\n | 6\n | ibivibiv/math_instruct | |
What is the product of 0.383 and -16.889?\n | -6.468487\n | ibivibiv/math_instruct | |
Let t = -0.62333 + 0.618. What is t rounded to four dps?\n | -0.0053\n | ibivibiv/math_instruct | |
Solve -9 = -5*k - 2*s, -11*s + 9*s - 15 = -3*k for k.\n | 3\n | ibivibiv/math_instruct | |
Express -5505*y**2 + 2753*y**2 + 29*y + 2748*y**2 in the form x + p*y**2 + q*y and give p.\n | -4\n | ibivibiv/math_instruct | |
Let r(t) = t. Let b(h) = h**2 + 5*h. Let q be b(-4). Let c(y) = -2*y. Calculate q*r(d) - c(d).\n | -2*d\n | ibivibiv/math_instruct | |
Calculate -9 + -95.\n | -104\n | ibivibiv/math_instruct | |
Let x = -29 + 30. Sort x, 5, -4 in increasing order.\n | -4, x, 5\n | ibivibiv/math_instruct | |
What is the result of the following expression?
2.2114 * (72.7499 + 91.3438) | 362.8768 | ibivibiv/math_instruct | |
((-40365)/17550)/(3/60)\n | -46\n | ibivibiv/math_instruct | |
Solve 0 = 7*d - d - 30 for d.\n | 5\n | ibivibiv/math_instruct | |
Let h = 6165 - 4126. Is h a prime number?\n | True\n | ibivibiv/math_instruct | |
Let 5*v**5 - 20655*v**4 + 9633535*v**3 + 26949957675*v**2 - 161995167360*v + 135035596800 = 0. What is v?\n | -867, 1, 5, 2496\n | ibivibiv/math_instruct | |
Four letters picked without replacement from djvdyv. Give prob of picking 4 j.\n | 0\n | ibivibiv/math_instruct | |
What is the result of the following expression?
50.9882 % (-15.506 + 63.7545) | 2.7397 | ibivibiv/math_instruct | |
Let c be (-1 + -4)*(-8)/10. Let y(u) = u - 3. Let p be y(4). Suppose 5 = 2*m + p. Sort m, c, -1 in increasing order.\n | -1, m, c\n | ibivibiv/math_instruct | |
A farmer has a rectangular field whose length is triple its width. Two ponds are located inside the field. The first pond is a square with each side equal to x meters length. The second one is a rectangle with a known width of 7 meters and length twice its width. It is known that the sum of the areas of ponds is one-th... | Let's denote the width of the field as \( w \) and the length as \( l \). According to the problem, the length is triple the width, so \( l = 3w \).
The area of the field is given by \( A_{field} = l \times w \), which becomes \( A_{field} = 3w \times w = 3w^2 \).
The first pond is a square with each side equal to \(... | ibivibiv/math_instruct | |
Let l be 190 - (2 - -2) - 5. Let k = l - 131. What is the highest common factor of 150 and k?\n | 50\n | ibivibiv/math_instruct | |
Let g(n) be the second derivative of -n**4/12 + 3*n**2/2 + 8*n. Let u be g(0). Solve u*x = -3*i + i + 5, x - 3 = -i for x.\n | -1\n | ibivibiv/math_instruct | |
b"What is the tth term of -3194, -6325, -9468, -12629, -15814, -19029?\n" | -t**3 - 3124*t - 69\n | ibivibiv/math_instruct | |
Let q = 36 - 65. Let n = 73 + q. Is n a multiple of 22?\n | True\n | ibivibiv/math_instruct | |
Solve -5*g**4 - 190*g**3 - 2340*g**2 - 8450*g + 10985 = 0.\n | -13, 1\n | ibivibiv/math_instruct | |
Let p = 0.25 + 0. Suppose -w = n - 31, 7*w - 3*w = 0. Suppose -n*t = -47 - 46. Which is the biggest value? (a) -0.2 (b) t (c) 2 (d) p\n | b\n | ibivibiv/math_instruct | |
Rearrange -10*w**2 - 8*w**4 - 30 - 4*w**3 + 54 + 5*w**2 + 4*w**2 - 3*w - 25 to z*w**2 + p*w**3 + a*w**4 + x*w + o and give p.\n | -4\n | ibivibiv/math_instruct | |
Collect the terms in -338*v - 337*v + 13954*v**3 + 1035*v - 360*v.\n | 13954*v**3\n | ibivibiv/math_instruct | |
Let f(r) be the first derivative of -r**3/3 + 5*r**2/2 + 2*r - 1. Suppose -9*g + 31 + 635 = 0. Suppose 0 = 2*u + 3*d - 23, 3*u + 52 = -2*d + g. Determine f(u).\n | 6\n | ibivibiv/math_instruct | |
Simplify (o/(o*o**(-3))*o)/o**(-1/3)*(o**(2/13))**(-9/5) assuming o is positive.\n | o**(791/195)\n | ibivibiv/math_instruct | |
Which is the second smallest value? (a) -4382 (b) -5 (c) 33/10\n | b\n | ibivibiv/math_instruct | |
What is the value of ((-230)/69)/((-15)/(-9))?\n | -2\n | ibivibiv/math_instruct | |
Let o = -6 + 4. Let j be ((-25)/o)/(2/4). Let d be (6/(-15))/((-1)/j). Solve -6*z + d = -z for z.\n | 2\n | ibivibiv/math_instruct | |
Total of 0.07 and 39425722209.\n | 39425722209.07\n | ibivibiv/math_instruct | |
Simplify (((j**2*j*j*j)/j)**(2/21)*((j/(j*j/(j*j*j**(-4/11)/j*j*j*j)))/j)/(j*(j*j*j**(1/3)*j)/j))**(-3) assuming j is positive.\n | j**(304/77)\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# derivative of the function y=e^x
• Dec 16th 2010, 09:52 AM
derivative of the function y=e^x
f(x)= (e^x +1)^2
I am not sure how to find the derivative of this one!
Do I (e^x +1)(e^x +1)?
• Dec 16th 2010, 09:55 AM
snowtea
Us... | The post discusses finding the derivative of the function f(x) = (e^x + 1)^2 using various methods including the chain rule. We will delve into these techniques, focusing on rigorous mathematical explanations while maintaining engagement through clear communication.
The Chain Rule: A Crucial Tool in Calculus
To unde... | ibivibiv/math_instruct | |
What is 9/(-6)*20/15?\n | -2\n | ibivibiv/math_instruct | |
What is 238 minutes before 11:22 PM?\n | 7:24 PM\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-53.775 % 10.517) / (17.261 - 96.986) | -0.1170 | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 119925 and 133250.\n | 1199250\n | ibivibiv/math_instruct | |
Find the second derivative of -26178*l**2*y**3 + 91*l**2*y**2 - 2*l*y**3 - 72277*y**2 + 4*y - 3 wrt l.\n | -52356*y**3 + 182*y**2\n | ibivibiv/math_instruct | |
Suppose y - r + 6*r - 3 = 0, 4*r + 44 = 5*y. Let w(l) = 10*l + 6. Let p be w(y). Let u = -38 + p. Is 16 a factor of u?\n | True\n | ibivibiv/math_instruct | |
Let a(s) = 0 - s**3 + 7 - 8 - s. Let f(x) = -x**3 + 8*x**2 + 2*x + 2. Let o(p) = -2*a(p) - f(p). What is the third derivative of o(r) wrt r?\n | 18\n | ibivibiv/math_instruct | |
What is the highest common divisor of 2580 and 222095?\n | 215\n | ibivibiv/math_instruct | |
Solve 2*p = z - 3, -4*z = -15*p + 13*p + 12 for z.\n | -5\n | ibivibiv/math_instruct | |
Let d(j) = 355661*j - 2. Let l(p) = -12*p. Calculate l(d(m)).\n | -4267932*m + 24\n | ibivibiv/math_instruct | |
What is the fourth root of 52708 to the nearest integer?\n | 15\n | ibivibiv/math_instruct | |
Let n(b) = -b**2 - 6*b - 4. Let h be n(-5). Let j = -3 + h. Let l be j + -1 + (-40)/(-14). What is the smallest value in -3, -5, l?\n | -5\n | ibivibiv/math_instruct | |
What is the fourth root of 1718 to the nearest integer?\n | 6\n | ibivibiv/math_instruct | |
Expand 2*p - 2*p + 2*p**3 - 8*p**3 + 0*p**3 - 10*p**3 + (8 - 3 - 12)*(-3*p**3 + 0*p**3 + 0*p**3).\n | 5*p**3\n | ibivibiv/math_instruct | |
Let p be ((-8)/(-12) - (-56)/(-12))/2. Put p, 0.06, 0.4 in decreasing order.\n | 0.4, 0.06, p\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-33.1554 * 21.3485 | -707.8181 | ibivibiv/math_instruct | |
What is the cube root of 7196167 to the nearest integer?\n | 193\n | ibivibiv/math_instruct | |
Suppose -80*j = -83*j + 3. Let t(x) = 33*x**2 - x + 1. Let y be t(j). Suppose d = 19 - 8. Calculate the highest common divisor of d and y.\n | 11\n | ibivibiv/math_instruct | |
Two letters picked without replacement from bkbpkipxxibxbkki. What is prob of sequence ip?\n | 1/40\n | ibivibiv/math_instruct | |
Sort -2/7, -4, -88078, 0.1 in descending order.\n | 0.1, -2/7, -4, -88078\n | ibivibiv/math_instruct | |
What is the difference between 0.468 and 0?\n | 0.468\n | ibivibiv/math_instruct | |
Let j(k) = -k**3 + 10*k**2 + 55*k - 264. Determine j(11).\n | 220\n | ibivibiv/math_instruct | |
Let u(t) = -7*t**3 + 2*t**2 - 4*t + 3. Let h be u(2). Let v = -268/5 - h. Let s = 0.02 + -3.02. What is the third smallest value in s, v, -2?\n | v\n | ibivibiv/math_instruct | |
Express -254*i + 2 + 5*i**2 - 189*i + 422*i - 6*i**3 in the form b*i**2 + v*i + d + j*i**3 and give v.\n | -21\n | ibivibiv/math_instruct | |
Factor -3*c**5 - 912*c**4 + 1836*c**3.\n | -3*c**3*(c - 2)*(c + 306)\n | ibivibiv/math_instruct | |
What is prob of picking 1 w, 1 s, and 1 o when three letters picked without replacement from oovojoosvscocoswjsoo?\n | 3/95\n | ibivibiv/math_instruct | |
Let t(w) be the first derivative of w**6/1620 + w**5/270 + w**4/108 + w**3 + 1. Let z(c) be the third derivative of t(c). Suppose z(b) = 0. What is b?\n | -1\n | ibivibiv/math_instruct | |
Put -4, 3377, -5145 in increasing order.\n | -5145, -4, 3377\n | ibivibiv/math_instruct | |
Solve -601*n - 4293 = 9649 - 119 for n.\n | -23\n | ibivibiv/math_instruct | |
Determine b, given that 15/2*b**2 + 0 + 9*b - 3/2*b**3 = 0.\n | -1, 0, 6\n | ibivibiv/math_instruct | |
Convert 0.6755713 millennia to years.\n | 675.5713\n | ibivibiv/math_instruct | |
Let x(n) be the second derivative of n**7/630 - n**6/144 - n**5/120 + n**4/6 + 5*n. Let t(p) be the third derivative of x(p). Is 23 a factor of t(-4)?\n | False\n | ibivibiv/math_instruct | |
Suppose -4*q + 9*q - 10 = 0. Find the third derivative of -6*n**2 + 7*n - 8*n**q - 19*n**2 - 6*n + 7*n**5 - 5*n**6 wrt n.\n | -600*n**3 + 420*n**2\n | ibivibiv/math_instruct | |
Does 41 divide 3835690?\n | False\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 9256 and 20.\n | 46280\n | ibivibiv/math_instruct | |
Suppose 44*q - 42*q - 8 = 0. Suppose -4*r - 20 = -3*o + 7*o, q*o + 20 = 4*r. Which is the second smallest value? (a) -3 (b) o (c) -0.3 (d) -1\n | a\n | ibivibiv/math_instruct | |
Let f(n) = -1 + 0*n**2 + 2*n - n**3 + 3 - n**2. Let j be f(-2). Find the third derivative of 8*w**2 - 11*w**2 - j*w**6 + 0*w**2 - w**6 wrt w.\n | -360*w**3\n | ibivibiv/math_instruct | |
Let c be (3/(-105)*-5)/((-6)/7). What is the closest to 0 in c, -2/21, -1/5?\n | -2/21\n | ibivibiv/math_instruct | |
What is -9331590 divided by 1866318?\n | -5\n | ibivibiv/math_instruct | |
Solve 4*z**2/3 - 512*z/3 + 1280 = 0 for z.\n | 8, 120\n | ibivibiv/math_instruct | |
Calculate the common denominator of 31/37888 and 21/176860.\n | 45276160\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 e when two letters picked without replacement from sdebnbrdr.\n | 0\n | ibivibiv/math_instruct | |
Let d(r) be the first derivative of r**4/4 + 5*r**3/3 - 3*r**2/2 + 5*r + 4. Let y be d(-5). What is the greatest common factor of y and 50?\n | 10\n | ibivibiv/math_instruct | |
Simplify (f**(1/26)*f**(-2/25))**(-14) assuming f is positive.\n | f**(189/325)\n | ibivibiv/math_instruct | |
Let y be 1 - (3 - 5) - 4/8. Let j(b) be the first derivative of 4 - 7/5*b**5 - 2*b + 5/4*b**4 - y*b**2 + 3*b**3. Find k such that j(k) = 0.\n | -1, -2/7, 1\n | ibivibiv/math_instruct | |
Suppose -3*b - 10 = 3*i - 4, -3*i + 4*b + 22 = 0. Suppose 2*v + 5*y + 0*y - 29 = 0, -i*v = -y - 35. Let m = -10 + v. Does 6 divide m?\n | False\n | ibivibiv/math_instruct | |
What is the product of -295634 and 3?\n | -886902\n | ibivibiv/math_instruct |
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