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Proving one Differentiation results to another

  1. Oct 27, 2008 #1
    1. The problem statement, all variables and given/known data
    I need in proving that the derivative (d[tex]^{n}[/tex]/dx[tex]^{n}[/tex])(sin4x + cos4x) = 4n-1 cos(4x + n[tex]\pi[/tex]/2)


    3. The attempt at a solution
    I understand implicit differentiation in basic problems but I get stump with the n exponent in the differentiation symbol; am I suppose to treat it as a 2nd, 3rd, 4th ... etc derivative?
    If thats so, how should I prove that the left equation equals the right one.

    So far I got to: 4(cos3x - sin3x)
     
  2. jcsd
  3. Oct 27, 2008 #2

    rock.freak667

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    Homework Helper

    If you want you could try proving it by mathematical induction.

    dn/dxn means the nth derivative
     
  4. Oct 28, 2008 #3

    HallsofIvy

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    For the "induction step" you need to prove that IF
    [tex]d^n 4(sin^4 x+ cos^4 x)= 4^{n-1} cos(4x+ n\pi/2)[/tex]
    then
    [tex]d^}{n+1} 4(sin^4 x+ cos^4 x)= 4^{n} cos(4x+ (n+1)\pi/2)[/tex]
    You should be able to do that just by differentiating the right hand side of the first equationl.
     
  5. Oct 28, 2008 #4
    Thank you, I understand now.
     
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