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Math Help - Hyperbolic functions

  1. #1
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    Hyperbolic functions

    I am really not understanding these. For example i have

    cosh6x+sinh6x

    i know that cosh is 1/2(e^x + e^-x) and sinh is 1/2(e^x - e^-x)

    so... what now?

    1/2(e^x + e^-x)6x+1/2(e^x - e^-x)6x
    ??
    i know somehow that 6x will be whats raised to it's power of the final answer which is e^6x but how?
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  2. #2
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    Quote Originally Posted by Frenchie View Post
    I am really not understanding these. For example i have

    cosh6x+sinh6x

    i know that cosh is 1/2(e^x + e^-x) and sinh is 1/2(e^x - e^-x)

    so... what now?

    1/2(e^x + e^-x)6x+1/2(e^x - e^-x)6x
    ??
    i know somehow that 6x will be whats raised to it's power of the final answer which is e^6x but how?


    \cosh6x=\frac{e^{6x}+e^{-6x}}{2} , and similar for \sinh6x

    Tonio
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  3. #3
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    what about y=ln(sech(8x+6))?

    answer is -8tanh(8x+6) but i'm not sure how to go about solving it
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  4. #4
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    First, do you really understand what your error in the first problem was? You wrote:

    "cosh is 1/2(e^x + e^-x) and sinh is 1/2(e^x - e^-x)"

    and then wrote

    "cosh(6x)+ sinh(6x)= 1/2(e^x + e^-x)6x+1/2(e^x - e^-x)6x"

    which is not only wrong it's "non-sense"- and it is important that you understand why. If that was not simply a typo or an oversight, then you have a serious misunderstanding of the notation.

    "cosh", by itself, is NOT what you had. cosh(x)= (1/2)(e^x+ e^-x) and the "(x)" is crucial. cosh(6x) is NOT "cosh" multiplied by "6x", it is cosh(x) with x replaced by 6x:
    cosh(6x)+ sinh(6x)= (1/2)(e^{6x}+ e^{-6x})+ (1/2)(e^{6x}- e^{-6x}).

    Adding those, cosh(6x)+ sin(6x)= e^{6x} because the e^{6x} terms add and the e^{-6x} terms cancel.

    Now you ask

    "what about y=ln(sech(8x+6))?

    answer is -8tanh(8x+6) but i'm not sure how to go about solving it"

    The answer to what question? Don't you think that is an important piece of information?

    I suspect you mean the answer to "the derivative of y with respect to x" but I don't know for sure.

    What is the derivative of ln(x)? What is the derivative of sech(x)= \frac{1}{cosh(x)}= \frac{2}{e^x+ e^{-x}}?
    Last edited by mr fantastic; November 2nd 2010 at 03:09 PM. Reason: Fixed math tag, added some spacing.
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