What is the derivative of cosh inverse x?

[JFonseka]

Homework Statement

Derive cosh$$^{-1}$$x

Homework Equations

None I know of.

The Attempt at a Solution

Well I vaguely remember that the inverse of this was something like

ln(x + $$\sqrt{x^2 - 1}$$)

If I derive this, I will get $$\frac{1}{\sqrt{x^2 - 1}}$$

Is that correct? Am I wrong to assume the equation for the inverse of cosh? Or do I need to prove that as well

 

[rock.freak667]

actually...$$\frac{d}{dx}arccoshx=\frac{1}{\sqrt{x^2-1}}$$

prove it by just letting y=arccoshx and then putting coshy=x and findind dy/dx
and use the identity cosh^2(x)-sinh^2(x)=1