Using the fact that $\displaystyle x \rightarrow logx$ is differentiable on $\displaystyle (0,\infty) $ with derivative $\displaystyle x \rightarrow \frac {1} {x} $ verify that $\displaystyle arctanh x=\frac {1} {2} log ( \frac {1+x} {1-x}) $ is differentiable and compute its derivative. Now I have no problem finding the derivative, however I'm not sure how to show it is differentiable. It shouldn't be too hard but I'm not too acquainted with the method. Thanks!!