I was just doing these for class last unit. You have to use the formula for deriving Inverse functions 1/f ' (g(x)) where f(x) is the inverse of g(x). In this case f (x)=sinch x and g(x)=arcsinch x (I don't know if it is legal to call it arcsinch, but I don't know how to write the math formulas on the computer) Anyway after this use the identity
cosh x= (1-(sinch x)^2)^1/2). try it from there and keep in mind it is similar to deriving inverse trig functions.