Thread: Help with hyperbolic inverse trig Dif/integration

My course seems to have some gaps and I'm having a hard time understanding hyperbolic inverse trig differentiation.

differentiate tanh^-1(sinx)
Book says switch x and y which will make the inverse go away

so I get tanh(siny) and Dx both sides
Dx = sec²h(siny)*Dx (sin y)
= sec²h(sin y) * cosy and thats where I get stuck. None of this seems to be right.



similarly the next problem is sinh^-1 (tan x) Hopefully if I can understand the mechanics of the first I can work the 2nd one a little smoother.
Thanks

Let



then



and now differentiate implicitly.