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Math Help - Help with this derivative?

  1. #1
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    Help with this derivative?

    It is from the infinite series section of the book, but I must have missed class this day because I don't know how to solve it. I don't need it worked out, just a point in the right direction. The problem is to compute the 7th derivative of

    1/14xcos(2x)

    I know he doesn't expect us to manually take the derivative 7 times, so what is the trick?
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  2. #2
    MHF Contributor chiph588@'s Avatar
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  3. #3
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    Thank you, but I understand how to manually compute the 7th derivative with the product rule. This is not what I am being tested on. It has something to do with series, but I can't find another example like this in my notes.
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  4. #4
    Member mybrohshi5's Avatar
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    That is going to get pretty messy (this is what wolfram believes the 7th derivative is http://www.wolframalpha.com/input/?i...cos%282x%29%29 ) but anyways i believe you would use:

    cos(x) =\displaystyle\sum_{n=0}^{\infty}(-1)^n * \frac{x^{2n}}{(2n)!}

    you would pull the \frac{1}{14x} out front of the summation and then plug in 2x for the x.

    then you would just do n=0 to n=6 i believe to get the 7th derivative.

    Hopefully someone can say if this is right or not cause i am not 100% positive....

    And since your function is 1/cosx this may not work for it but its all i could think of doing from a SERIES
    Last edited by mybrohshi5; April 29th 2010 at 01:29 PM.
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  5. #5
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    I think the series you wrote is actually sin, not cos. Can anyone clarify how to do this?
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  6. #6
    Member mybrohshi5's Avatar
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    Yeah sorry i edited it so now it is cos. Hopefully someone smarter than me will see this post and be able to help you out a little more

    is your function \frac{1}{14}xcos(2x) or is it \frac{1}{14xcos(2x)}

    if it is \frac{1}{14}xcos(2x) i do think you can use this series i stated.

    You would do n=o to n=7 to get 7th derivative so this is what i came up with.

    for n=0 ----- \frac{1}{14}*1

    n=1 ------ \frac{1}{14}*(-1)*\frac{4x^2}{2!}

    n=2 ------ \frac{1}{14}*(1)*\frac{4^4x^4}{4!}

    keep doing this until n=7 then just reduce everything and i believe you would get your 7th derivative.

    Someone please check this
    Last edited by mybrohshi5; April 29th 2010 at 01:47 PM.
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  7. #7
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    If you are indeed correct, then I think I understand. Thank you! And it is (1/14)x cos(2x). I should have made that clear from the beginning.
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  8. #8
    Member mybrohshi5's Avatar
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    when do you need this done by?

    I can ask someone tomorrow who will know how to do it and can post it by tomorrow afternoon.
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  9. #9
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    Test is tomorrow, but no worries.
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  10. #10
    Member mybrohshi5's Avatar
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    oh aight well good luck on the test.

    Hopefully someone will look over this post and answer the question for you.
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  11. #11
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    How do you find high order derivatives using series?

    Thanks!
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