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Double derivative of tan(x)

  1. Feb 28, 2010 #1
    1. The problem statement, all variables and given/known data
    the question asked to prove that the double derivaitve of y=tan(x) is...
    2y(1+y^2)
    eg. 2tanx(1+tan^2(x))



    2. Relevant equations



    3. The attempt at a solution

    I was able to get the first derivative ( i think)
    y=tan(x)
    =(sin(x))/(cos(x))

    dy/dx=(cos(x)cos(x)-(sin(x)(-sin(x))))/cos^2(x)
    =(cos^2(x)+sin^2(x))/cos^2(x)
    =1/cos^2(x)

    from here i am not to sure how to get the second derivative...
     
  2. jcsd
  3. Feb 28, 2010 #2

    Borek

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    Staff: Mentor

    So far so good, just differentiate cos-2x.
     
  4. Feb 28, 2010 #3
    So would i use the quotient rule to do that or something else?? like the chain rule??
     
  5. Feb 28, 2010 #4
    ok iv done that i get
    2sin(x)/cos^3(x)
    now iv got the double derivative i cant see how to simplify it to get 2tanx(1+tan^2(x))
     
  6. Feb 28, 2010 #5

    Borek

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    Staff: Mentor

    All I can tell is that

    [tex]\frac {2 \sin x} {\cos^3 x} = \frac {2 \tan x } {\cos^2 x} [/tex]

    is a correct second derivative.
     
  7. Feb 28, 2010 #6
    ok thanks for the help i should be able to get it from here
     
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