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Find derivative

  1. Jan 17, 2012 #1
    1. The problem statement, all variables and given/known data
    [tex]\frac{d^{2n}}{dx^{2n}}\cos x[/tex]

    [tex]n \in N[/tex]


    2. Relevant equations
    [tex]\cos x=\sum^{\infty}_{k=0}(-1)^k\frac{x^{2k}}{(2k)!}[/tex]


    3. The attempt at a solution
    [tex]\frac{d^{2n}}{dx^{2n}}x^{2n}=(2n)![/tex]

    But k is different that [tex]n[/tex]. I don't have a clue how to solve that.
     
  2. jcsd
  3. Jan 17, 2012 #2

    Char. Limit

    User Avatar
    Gold Member

    Here's a recommendation: Check the derivative for certain small values of n and see if you can find a pattern. I recommend n=0, n=1, and n=2. Then just remember that

    [tex]\frac{d^{n+4}}{d x^{n+4}} cos(x) = \frac{d^n}{d x^n} cos(x)[/tex]

    And that should finish your problem.
     
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