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Differentiating tanh

  1. Mar 6, 2005 #1
    I've been given a couple of problems to do, which i'm unable to because before looking at the queston i'd never even HEARD of tanh, which is just... lovely of my lecturer :grumpy:

    anyway, i had a look around on some websites & fiddled around with it on my calculator and i now have some idea what its all about... and i do mean some. But unfortunately all i could find was d/dx(tanhx) = 1 - tanh^2x
    My problems are rather more complex than the variable sitting by itself... I'd like to have a go at the actual problems myself though, so if someone could work through the one below, which is sort of similar, and explain any rules they use... it should be helpful.

    f(x) = 2tanh(x(3/4)^(1/2))
    f '(x) = ?

  2. jcsd
  3. Mar 6, 2005 #2


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    Use the definition:[tex] \tanh x=:\frac{\sinh x}{\cosh x} [/tex].And of course,the chain rule.

  4. Mar 6, 2005 #3
    d/dx(tanhx) = 1 - tanh^2x
    Also equivalent to sech^2x, so you could just use that...
    f(x) = 2tanh(x(3/4)^(1/2))
    f '(x) = ?

    When you see something as ugly and unattractive as that, you should immediately say "Oh God, not the chain rule!"
    And... I guess that's pretty much all you need to doing this one.
    Happy differentiating... integrating is the devil. :devil:
  5. Mar 6, 2005 #4


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    do you have a book? does it have an index? is it really your lecturer's fault if you have never heard of tanh?

    have you heard of sinh, cosh? if so can you guess the definition of tanh?

    to the best of my memory, after 40 years,

    sin(x) = (1/2i)[e^(ix) - e^(-ix)], cos(x) = (1/2)(e^(ix)+e^(-ix)]

    sinh(x) = (1/2)[e^(x) - e^(-x)], cosh(x) = (1/2)(e^(x)+e^(-x)].

    presumaby tanh = sinh/cosh.

    compare that with what you can find.
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