# Derivative of cosh inverse x

1. Nov 10, 2007

### JFonseka

1. The problem statement, all variables and given/known data

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

2. Relevant equations

None I know of.
3. 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

2. Nov 11, 2007

### 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

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