Derivative of Arccosecant of Function

Theorem
Let $u$ be a differentiable real function of $x$ such that $\size u > 1$.

Then:
 * $\map {\dfrac \d {\d x} } {\arccsc u} = -\dfrac 1 {\size u \sqrt {u^2 - 1} } \dfrac {\d u} {\d x}$

where $\arcsec$ denotes the arccosecant of $x$.

Also see

 * Derivative of Arcsine of Function
 * Derivative of Arccosine of Function


 * Derivative of Arctangent of Function
 * Derivative of Arccotangent of Function


 * Derivative of Arcsecant of Function