Derivative of Inverse Hyperbolic Tangent Function

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

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

where $\size u < 1$ where $\tanh^{-1}$ is the inverse hyperbolic tangent.

Also see

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


 * Derivative of Inverse Hyperbolic Cotangent Function


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