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Calculus Questions - All Grades

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The Calculus questions below are in the following grade levels:
Grades: 11 12 College
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Grade 11 :: Calculus by jthompson85
[math]f(x)=3x^-3 + 8x^-2 - x^-1 + 8[/math]
  • [math]f'(x)=-9x^-4 -16x^-3 + x^-2[/math]
College :: Calculus by Narishm
What is the derivative of 21?
  1. 0
  2. 21
  3. 7
  4. 3
Grade 11 :: Calculus by jthompson85
Find the derivative:
[math]f(x) = (4x^2-3x+2)/(2x-1[/math]
  • [math]f'(x)=[(2x-1)(8x-3)-(4x^2-3x+2)(2)]/(2x-1)^2[/math]
Grade 11 :: Calculus by jthompson85
[math]f(x)=(5x^4-2x^2 + 4)^(1/3[/math]
  • [math]f'(x)=1/3(5x^4-2x^2+4)^(-2/3)(20x^3-4x)[/math]
College :: Initial Value Problems by BacMan
Solve [math]y''=12x^2[/math] where [math]y'(0) = 15[/math] and [math]y(0) = 13[/math]
  • Itegrate:
    [math]y' = int12x^2dx = 4x^3 + c_1[/math]

    Using the first condition [math]y'(0) = 15[/math]:
    [math]4(0)^3 + c_1 = 15[/math]
    [math]c_1 = 15[/math]

    Therefore, the differential equation is:
    [math]y' = 4x^3 + 15[/math]

    Integrate again:
    [math]y = int(4x^3 + 15)dx = x^4 + 15x + c_2[/math]

    Using the second condition [math]y(0) = 13[/math]:
    [math]0^4 + 15*0 + c_2 = 13[/math]
    [math]c_2 = 13[/math]

    The answer is:
    [math]y = x^4 + 15x + 13[/math]
Grade 12 :: Calculus by jthompson85
[math]f(x) = sqrt tan(3x)[/math]
  • [math]f'(x) =1/(2(sqrttan(3x)))(sec^2(3x))(3)[/math]
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