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Help on derivatives

  1. Oct 30, 2011 #1
    1. The problem statement, all variables and given/known data

    Let h(t) = tan(3t+7)

    Find h'(t) and h''(t)

    I found h'(t) which is equal to 3(sec(3t+7))^2

    But I can't seem to find h''(t)

    How do I find the derivative of this? Could someone please teach me?

    Is it a composition function? If it is, I think I see 4 functions.

    Thanks in advance.
     
  2. jcsd
  3. Oct 30, 2011 #2

    Ibix

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    There are at least two ways to do it. The key observation is that sec(x)=1/cos(x). That should give you the answer using standard tools for handling derivatives of functions.
     
  4. Oct 30, 2011 #3
    Yeah, I knew that sec(x) = 1/cos(x)

    and I still couln't figure out what to do
     
  5. Oct 30, 2011 #4

    SteamKing

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    Maybe if you substitute 1/cos for sec in h'(t) that will give you a clue.
     
  6. Oct 30, 2011 #5

    Mark44

    Staff: Mentor

    Or you can differentiate sec(u) directly, using the formula d/dt(sec(u)) = sec(u)tan(u) * du/dt.
     
  7. Oct 30, 2011 #6

    Ibix

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    Science Advisor

    You have already used what I would call the Chain Rule:
    [tex]\frac{d}{dx}f_1(f_2(x))=f_1'(f_2(x))f_2'(x)[/tex]
    to get h'(x). All you need to realise is that you can nest functions as deep as you like - just replace [itex]x[/itex] with [itex]f_3(x)[/itex] throughout and tack [itex]f_3'(x)[/itex] on the end:
    [tex]\frac{d}{dx}f_1(f_2(f_3(x)))=f_1'(f_2(f_3(x)))f_2'(f_3(x))f_3(x)[/tex]
    Then you need to work out what each of the [itex]f[/itex]s is here and dive in.
     
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