Derivative of Inverse Hyperbolic Secant Function

Theorem
Let $u$ be a differentiable real function of $x$.

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

where $0 < u < 1$ where $\sech^{-1}$ is the inverse hyperbolic secant.

Also see

 * Derivative of Inverse Hyperbolic Sine Function
 * Derivative of Real Area Hyperbolic Cosine of Function


 * Derivative of Inverse Hyperbolic Tangent Function
 * Derivative of Inverse Hyperbolic Cotangent Function


 * Derivative of Inverse Hyperbolic Cosecant Function