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Math Help - help 2nd derivative

  1. #1
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    help 2nd derivative

    Find \frac {d^2y} {dx^2} for y = cos^2 4x
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Samantha View Post
    Find \frac {d^2y} {dx^2} for y = cos^2 4x
    \frac {d^2 y}{dx^2} means the second derivative. so you take the derivative of y and then take the derivative of the result, and that's your answer.

    is it the derivative you need help with, or did you not know that was what you should do?
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    \frac {d^2 y}{dx^2} means the second derivative. so you take the derivative of y and then take the derivative of the result, and that's your answer.

    is it the derivative you need help with, or did you not know that was what you should do?
    I don't know how to do it...

    I have a hard time with derivatives...
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  4. #4
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Samantha View Post
    Find \frac {d^2y} {dx^2} for y = cos^2 4x
    \frac {d^2y} {dx^2} for y = cos^2 4x

    Use the chain rule.

     y = cos^2 4x
     \frac{dy}{dx} = 2cos(4x) . (-sin(4x)) . 4
     = -8cos(4x)(sin(4x))

    You must derive twice. But use the product rule now.

     \frac{dy}{dx} (-8cos(4x)(sin(4x))) =  -8cos(4x)' . (sin(4x)) + -8cos(4x) . (sin(4x))'

     = (-32(-sin(4x))) . (sin(4x)) + (-8(cos(4x)) . (4(cos(4x)))

    I hope that's right...
    I don't have much experience with this. Jhevon's still helping me get the hang of these things...
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  5. #5
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    So the answer is - 32 cos 8x?
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  6. #6
    Newbie servantes135's Avatar
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    Quote Originally Posted by janvdl View Post
    \frac {d^2y} {dx^2} for y = cos^2 4x

    Use the chain rule.

     y = cos^2 4x
     \frac{dy}{dx} = 2cos(4x) . (-sin(4x)) . 4
     = -8cos(4x)(sin(4x))

    You must derive twice. But use the product rule now.

     \frac{dy}{dx} (-8cos(4x)(sin(4x))) = -8cos(4x)' . (sin(4x)) + -8cos(4x) . (sin(4x))'

     = (-32(-sin(4x))) . (sin(4x)) + (-8(cos(4x)) . (4(cos(4x)))

    I hope that's right...
    I don't have much experience with this. Jhevon's still helping me get the hang of these things...
    Verry close.
    the answer is

    (-32*-sin^2(4x))+(-32*cos^2(4x))

    -32*(cos^2(4x)-sin^2(4x))

    with the double angle form
    cos^2(x)-sin^2(x)= cos(2x)

    we can simplify this
    -32cos(8x)
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  7. #7
    Bar0n janvdl's Avatar
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    Quote Originally Posted by servantes135 View Post
    Verry close.
    the answer is

    (-32*-sin^2(4x))+(-32*cos^2(4x))

    -32*(cos^2(4x)-sin^2(4x))

    with the double angle form
    cos^2(x)-sin^2(x)= cos(2x)

    we can simplify this
    -32cos(8x)
    Didn't see that! Thanks!
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