Derivative of Real Area Hyperbolic Secant of x over a

Theorem

 * $\dfrac {\map \d {\map \arsech {\frac x a} } } {\d x} = \dfrac {-a} {x \sqrt{a^2 - x^2} }$

where $0 < x < a$.

Proof
Let $0 < x < a$.

Then $0 < \dfrac x a < 1$ and so:

$\arsech \dfrac x a$ is not defined when $x \le 0$ or $x \ge a$.

Also see

 * Derivative of $\arsinh \dfrac x a$


 * Derivative of $\arcosh \dfrac x a$


 * Derivative of $\artanh \dfrac x a$


 * Derivative of $\arcoth \dfrac x a$


 * Derivative of $\arcsch \dfrac x a$