Deriving the formula for arctanh(x)

[hlechte]

Homework Statement

"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

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

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.