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Chain Rule Again, Sorry

  1. Aug 1, 2010 #1
    1. The problem statement, all variables and given/known data

    tan^3(x) + tan(x^3)

    2. Relevant equations



    3. The attempt at a solution

    tan^3(x) + sec^2(x^3) + 3x^2


    Im not sure how to do the tan^3(x) and not even sure I did the tan(x^3) right
     
  2. jcsd
  3. Aug 1, 2010 #2

    lanedance

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    Homework Helper

    the first term is as follows
    [tex] \frac{d}{dx} (tan(x))^3 = 3 tan^2(x)\frac{d (tan(x))}{dx} =..[/tex]

    here assume you have
    [tex] g(x) = x^3 [/tex]
    [tex] f(x) = tan(x) [/tex]

    and you know
    [tex] g(x) = 3x^2 [/tex]
    [tex] f(x) = sec(x) [/tex]

    in this form it becomes
    [tex] g(f(x)) = (tan(x))^3 =..[/tex]

    [tex]\frac{d}{dx} g(f(x)) = g'(f(x))f'(x) = ...[/tex]

    finish this & try the 2nd term again as its not correct either
     
  4. Aug 1, 2010 #3

    lanedance

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    Homework Helper

    expanded above
     
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