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D.w.r.t.x ln[ln tanh x]

  1. Dec 6, 2011 #1

    sharks

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    The problem statement, all variables and given/known data
    D.w.r.t.x ln[ln tanh x]

    The attempt at a solution
    So, here is what i've done:

    Since differentiating ln x is 1/x

    The answer is: (1/ln tanh x).(tanh x).sech(^2)x

    What do you think? The answer is not the above though.
     
  2. jcsd
  3. Dec 6, 2011 #2

    sharks

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    OK, i've made a typo error in the above, as my actual solution is:

    The answer is: (1/ln tanh x).(1/tanh x).sech(^2)x

    It's still not the correct answer though, so i'm staring into space.
     
  4. Dec 6, 2011 #3

    I like Serena

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    Hi sharks! :smile:

    Your answer looks right to me.
    Is this for some on-line website that has difficulty parsing correct answers?
     
  5. Dec 6, 2011 #4

    sharks

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    Here is the answer (from my maths manual): Not defined. :redface:
     
  6. Dec 6, 2011 #5
    Your "(1/ln tanh x).(1/tanh x).sech(^2)x" answer is correct, but you can use trig identities to reduce the "(1/tanh x).sech(^2)x" part to a cosh function. Might that be part of the confusion?
     
  7. Dec 6, 2011 #6

    I like Serena

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    Ah, I see.
    It's a trick question.
    Your original function ln[ln tanh x] is not well defined anywhere, since tanh x < 1.
    Since the original function is not properly defined, neither is its derivative.
     
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