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Math Help - Help with hyperbolic inverse trig Dif/integration

  1. #1
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    Help with hyperbolic inverse trig Dif/integration

    My course seems to have some gaps and I'm having a hard time understanding hyperbolic inverse trig differentiation.

    differentiate tanh-1(sinx)
    Book says switch x and y which will make the inverse go away

    so I get tanh(siny) and Dx both sides
    Dx = sec2h(siny)*Dx (sin y)
    = sec2h(sin y) * cosy and thats where I get stuck. None of this seems to be right.



    similarly the next problem is sinh-1 (tan x) Hopefully if I can understand the mechanics of the first I can work the 2nd one a little smoother.
    Thanks
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  2. #2
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    Re: Help with hyperbolic inverse trig Dif/integration

    Let

    y = \tanh^{-1}(\sin x),

    then

    \tanh y = \sin x,

    and now differentiate implicitly.
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