# Help with hyperbolic inverse trig Dif/integration

• October 7th 2012, 09:03 AM
culpepper
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
• October 7th 2012, 09:39 AM
BobP
Re: Help with hyperbolic inverse trig Dif/integration
Let

$y = \tanh^{-1}(\sin x),$

then

$\tanh y = \sin x,$

and now differentiate implicitly.