d/dx [tanh^-1 (coshx)]

Question

My teacher got sinhx/1+cosh^2 x as the answer but I’m getting -cschx as my answer because can‘t sinhx/1-cosh^2 x be sinplified using identities? Which answer is correct? 

Answer 1

I do not use hyperbolic functions often...but let's try this

 

f(x) = tanh^-1(cosh x)

 

chain rule: f'(x) = (1/(1 - cosh² x) * sinh x = sinh x/(-sinh² x) = -csch x

 

I may be wrong but I agree with you.  Please get your teacher to show his/her work and if you have the time, please show me.