Derivative of Real Area Hyperbolic Cosine of Function

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

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

where $u > 1$ where $\cosh^{-1}$ is the inverse hyperbolic cosine.

Also see

 * Derivative of Inverse Hyperbolic Sine Function


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


 * Derivative of Inverse Hyperbolic Secant Function
 * Derivative of Inverse Hyperbolic Cosecant Function