Derivative of Hyperbolic Cosecant

Theorem

 * $\map {\dfrac \d {\d x} } {\csch x} = -\csch x \coth x$

where:
 * $\coth x$ denotes the hyperbolic cotangent and $\csch z$ denotes the hyperbolic cosecant.
 * $x \in \R_{\ne 0}$

Proof
It is noted that at $x = 0$, $\csch x$ is undefined.

Hence the restriction of the domain.

Also see

 * Derivative of Hyperbolic Sine
 * Derivative of Hyperbolic Cosine


 * Derivative of Hyperbolic Tangent
 * Derivative of Hyperbolic Cotangent


 * Derivative of Hyperbolic Secant