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Differentiating Hyperbolic Functions

  1. Apr 17, 2010 #1

    BoT

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    1. Differentiate cosh(x) using first principles



    2. cosh(x) = (e^x+e^-x)/2


    From previous exercises, I know the answer will be sinh(x)= (e^x-e^-x)/2 but I cannot get to the answer.
    I seem to be left with the equation: lim h ---> 0 (e^2x*e^2h +1-e^h*2e^x +e^h)/(2h*e^x*e^h)
    But when you make h=0 , it becomes underfined???
    1. The problem statement, all variables and given/known data
     
  2. jcsd
  3. Apr 17, 2010 #2

    rock.freak667

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    Homework Helper

    Where did you get e2x and whatnot from?

    Just simplify

    [tex]\frac{e^{x+h}+e^{-(x+h)}-(e^x+e^{-x})}{2h}[/tex]


    and then factorize.
     
  4. Apr 17, 2010 #3

    BoT

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    I got it to

    ex*eh+e-x*e-h -ex -e-x/ 2h

    But how do I simplify this?
    This is the part that always screws me up!
     
  5. Apr 17, 2010 #4

    rock.freak667

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    Homework Helper

    Factor out ex from ex*eh and ex. Do a similar exercise with e-x from the terms.

    Then compute the limits.
     
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