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Math Help - The second derivative of Y= x(Sinx)

  1. #1
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    Post The second derivative of Y= x(Sinx)

    For this problem I already know what the answer is. I just don't know how to get to it. The question is...

    Find the second derivative of Y = x(Sinx)

    I know that to get it to Y' I use the product rule which would translate into
    [x(sinx)' +x'(Sinx) which gets me...

    Y' = x(Cosx) + (Sinx)

    This is the part I am unsure of. What I did after that was
    [x(Cosx)' +x'(Cosx) + (Sinx)'] Which gave me...

    x(-Sinx) + (Cosx) + (Cosx)

    My end result was 2(Cosx) + x(-Sinx)

    The answer is suppose to be...
    Y''
    = 2(Cosx) - x(Sinx)

    Can anyone tell me what I did wrong, and explain to me how to get the right answer?
    Last edited by Brazuca; June 20th 2009 at 02:00 PM. Reason: make it look better
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  2. #2
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    Quote Originally Posted by Brazuca View Post
    For this problem I already know what the answer is. I just don't know how to get to it. The question is...

    Find the second derivative of Y = x(Sinx)

    I know that to get it to Y' I use the product rule which would translate into
    [x(sinx)' +x'(Sinx) which gets me...

    Y' = x(Cosx) + (Sinx)

    This is the part I am unsure of. What I did after that was
    [x(Cosx)' +x'(Cosx) + (Sinx)'] Which gave me...

    x(-Sinx) + (Cosx) + (Cosx)

    My end result was 2(Cosx) + x(-Sinx)

    The answer is suppose to be...
    Y''
    = 2(Cosx) - x(Sinx)

    Can anyone tell me what I did wrong, and explain to me how to get the right answer?
    2(Cosx) + x(-Sinx) = 2cos(x) + x*-sin(x) = 2cos(x) - xsin(x)
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  3. #3
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    Thanks, that was the last piece of the puzzle for me to understand this and two other problems.
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