Saturday, March 21, 2009

Question set 5

  1. Let f(x) = sin x. Find the first 3 derivatives of f.
  2. Let f(t) = 5 cos t. Find the first 4 derivatives of f.
  3. Let f(x) = 3cos x + 5x. Find the first 3 derivatives of f.
  4. Let f(t) = 2t + sin t. Find the first 3 derivatives of f.
  5. Let f(t) = 1/t2 - sin t. Find the first 2 derivatives of f.
  6. Let f(x) = sin x - cos x. Find the first 4 derivatives of f.
  7. Let f(x) = 2sin x + 3cos x. Find the first 4 derivatives of f.
  8. Let f(x) = 4sin x + 1/x. Find the first 3 derivatives of f.
  9. Let f(t) = -3sin t + 1/2 cos t. Find the first 3 derivatives of f.
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7 comments:

  1. poopsiepumkinpieMarch 22, 2009 at 9:21 AM

    (1) let y= sin x

    dy/dx= cos x

    d^2y/dx^2= - sinx

    d^3y/dx^3= -cos x


    (2)let y=5 cos t
    dy/dx= 5 -sin t

    d^2y/dx^2= 5 -cos t

    d^3y/dx^3= 5 sin t

    d^4y/dx^4= 5 cos t

    ReplyDelete
  2. mysticwings*March 22, 2009 at 7:20 PM

    no 3
    y = 3 cos x + 5x

    dy/dx = 3 -sin x + 5

    d^2y/dx^2 = 3 -cos x

    d^3y/dx^3 = 3 sin x

    ReplyDelete
  3. mysticwings*March 22, 2009 at 7:22 PM

    no 4

    y = 2t + sint

    dy/dt = 2 + cost

    d^2y/dx^2 = -sint

    ReplyDelete
  4. mysticwings*March 22, 2009 at 7:28 PM

    no 5

    y = 1/t^2 - sint

    y = t^-2 - sint

    dy/dt = -2t^-3 - cost

    d^2y/d^2t = 6t^-4 + sint

    ReplyDelete
  5. ghetto_celebMarch 24, 2009 at 12:32 AM

    NO.6

    Let f(x) = sin x - cos x. Find the first 4 derivatives of f.

    would let f(x) = y

    rewrite

    y = sin x - cos x

    dy/dx of sin x = cos x and dy/dx of cos x = -sin x

    so dy/dx = cos x + sin x

    d^2y/dx^2 = -sin x + cos x

    d^3y/dx^3 = -cos x - sin x

    d^4y/dx^4 = sinx - cos x

    ReplyDelete
  6. Swanky ThingMarch 24, 2009 at 4:04 PM

    1)Let f(x) = sin x. Find the first 3 derivatives of f.
    let y= sin x
    First derivative...........dy/dx= cos x
    Second derivative..........d^2y/dx^2= - sinx
    Third derivative...........d^3y/dx^3= -cos x

    2)Let f(t) = 5 cos t. Find the first 4 derivatives of f.
    let y=5 cos t
    First Derivative...........dy/dx= 5 -sin t
    Second derivative..........d^2y/dx^2= 5 -cos t
    Third derivative...........d^3y/dx^3= 5 sin t
    Forth derivative...........d^4y/dx^4= 5 cos t

    3)Let f(x) = 3cos x + 5x. Find the first 3 derivatives of f.
    y = 3cos x + 5x
    First derivative...........dy/dx = 3 -sin x + 5
    Second derivative..........d^2y/dx^2 = 3 -cos x
    Third derivative...........d^3y/dx^3 = 3 sin x


    9)Let f(t) = -3sin t + 1/2 cos t. Find the first 3 derivatives of f.
    ....First derivative
    dy/dx = 3 -cos t - 1/2 sin t
    ....Second derivative
    d^2y/dx^2 = 3 sin t + 1/2 cos t
    ....Third derivatived
    d^3y/dx^3 = 3 cos t + 1/2 -sin t

    ReplyDelete
  7. ~*DJ HalfTime*~April 3, 2009 at 10:33 AM

    question 8

    f(x) = 4sinx + 1/x
    f(x) = 4sinx + x^-1

    1st derivative
    dy/dx = 4cosx - x^-2

    2nd derivative
    d^2y/dx^2 = -4sinx + 2x^-3

    3rd derivative
    d^2y/dx^2 = -4cosx -6x^-4

    ReplyDelete

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