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Inverse hyperbolic sin derivation

  1. Sep 15, 2011 #1
    1. The problem statement, all variables and given/known data
    derive the formula inverse sinhx = ln(x+sqrt(x^2+1)) for all real x


    2. Relevant equations
    sinhx=(e^x-e^-x)/2 ?



    3. The attempt at a solution
    i have been staring at this for awhile and i dont know how to start
    what should be the first step towards deriving that formula? i just want a hint to get started
     
  2. jcsd
  3. Sep 15, 2011 #2
    Let f(x)=(ex-e-x)/2

    (A function is a map from x→f(x). The inverse is therefore a map from f(x)→x. Therefore, our goal is to isolate x from the above equation.)

    f(x)=(ex-e-x)/2

    2f(x)=ex-e-x

    2f(x)ex=(ex-e-x)ex

    2f(x)ex=e2x-1

    0 = e2x-2f(x)ex-1

    Use the quadratic formula to find ex.
     
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