# Deriving the formula for arctanh(x)

1. Aug 19, 2008

### hlechte

1. The problem statement, all variables and given/known data

"starting from the definition of tanhx in terms of exponentials, prove that...

arctanh(x)=1/2log((1+x)/(1-x))

This is such a simple equation but I'm having a hard time proving it, can anyone help?

Cheers

2. Relevant equations

3. The attempt at a solution

2. Aug 19, 2008

### HallsofIvy

Staff Emeritus
If y= tanh(x) then
$$y= \frac{e^x- e^{-x}}{e^x+ e^{-x}}$$
Now use the standard method of finding an inverse function: solve that equation for x.