I know that $\displaystyle x$ $\displaystyle \mapsto$ $\displaystyle logx$

is differentiable on (0,$\displaystyle \infty$) with derivative $\displaystyle 1/x$

but how do I use this to prove that $\displaystyle arctanhx$=$\displaystyle (1/2)$$\displaystyle log$$\displaystyle (1+x)/(1-x)$=$\displaystyle (1/2)$$\displaystyle log(1+x)$ - $\displaystyle (1/2)$$\displaystyle log(1-x)$

is also differentiable?