y = tanh^-1 x + ln sqrt(1-x^2)

then i know tanh^-1 = 1/2ln (1+x)/(1-x) + ln sqrt(1-x^2) but lost pretty much there after.

then a none hyperbolic derivative

y = x cos ^1 x - sqrt(1-x^2)

do I use the chain rule in both of these cases? or if not what rule would I use ?