What is the $n$th derivative of $\coth(x)$?

Question

I would like to know the $n$th derivative of the Hyperbolic Cotangent, i. e., $\frac{\partial^n}{\partial x^n} \coth( x )$. So far, I have only found an expression for the $n$th derivative of the Hyperbolic Tangent on this website (see Eq. (8)). Maybe there is some obvious way to derive one from another which I am not aware of?

Answer 1

Hint: $$ \coth(x)= \tanh(x+i\pi/2) $$