What is a purely geometric proof of the derivatives of the inverse hyperbolic trig functions? I saw this post by John Hilbert here. and a answer from Blue here. That gave me a new question What are some purely geometric proofs of inverse hyperbolic trigonometric functions derivatives?
I do not want to use the fact that $\cos(xi)=\cosh(x)$ and then using implicit differentiation because I already know how to use that method. I want it to be proved using the geometry of a hyperbola.