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# Logarithmic form of artanh watch

1. Hi, just doing a bit on hyperbolics and a question has asked me to derive the logarithmic form of artanh. I can derive arsinh and arcosh but I'm fairly stumped with this one :/.
2. take the bottom fraction over to the otherside. rearrange for e^2x then take logs.

we then have that x=arctanhy=something else...
3. IIRC, it's easier to derive that the logarithmic forms of arcsin and arccos.

Let y = tanh x = sinh x / cosh x; so ; can you rearrange for x?

[the reason it's easier is that one doesn't need to solve a quadratic, it can be rearranged linearly.]
4. yay i got it , artanhx = 1/2 ln((x+1)/(1-x))
5. i did this question today, fun times

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Updated: February 13, 2010
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