Find the slope of the tangent line to the graph e^{xy}-x=0 at x=1. Let y=frac{e^x-e^{-x}/{e^x+e^{-x}. Show that the tangent lines at x=1 and x=-1 are parallel.

Answer 1

Let f(x) = [ e^x−e^-x ] / [ e^x+e^-x ]

Find f ' (x) .

Find f ' (1) and f ' (-1) and observe that they are equal, that is the slopes of the tangent lines are equal

therefore the tangent lines must be parallel