Is the Derivative of ln[ln tanh x] Well-Defined?

[DryRun]

Homework Statement
D.w.r.t.x ln[ln tanh x]

The attempt at a solution
So, here is what I've done:

Since differentiating ln x is 1/x

The answer is: (1/ln tanh x).(tanh x).sech(^2)x

What do you think? The answer is not the above though.

 

[DryRun]

OK, I've made a typo error in the above, as my actual solution is:

The answer is: (1/ln tanh x).(1/tanh x).sech(^2)x

It's still not the correct answer though, so I'm staring into space.

 

[I like Serena]

Hi sharks!

Your answer looks right to me.
Is this for some on-line website that has difficulty parsing correct answers?

 

[DryRun]

Here is the answer (from my maths manual): Not defined.

 

[obafgkmrns]

Your "(1/ln tanh x).(1/tanh x).sech(^2)x" answer is correct, but you can use trig identities to reduce the "(1/tanh x).sech(^2)x" part to a cosh function. Might that be part of the confusion?

 

[I like Serena]

Ah, I see.
It's a trick question.
Your original function ln[ln tanh x] is not well defined anywhere, since tanh x < 1.
Since the original function is not properly defined, neither is its derivative.