We need to find the derivative of \(\operatorname{csch}(x)\):
\[\frac{d}{dx}\operatorname{csch}(x) = \frac{d}{dx}\frac{1}{\sinh(x)}\]
If we derivative this:
\[\frac{d}{dx}\operatorname{csch}(x) = \frac{d}{dx} (\cosh(x))^{-1} = -(\sinh(x))^{-2} (\cosh(x)) \]
This means:
\[\frac{d}{dx}\operatorname{csch}(x) = -(\sinh(x))^{-1}(\coth(x)) = - \operatorname{csch}(x)\coth(x) \]