Derivative of Real Area Hyperbolic Sine of x over a

Theorem

 * $\dfrac {\mathrm d \left({\sinh^{-1} \left({\frac x a}\right)}\right)} {\mathrm d x} = \dfrac 1 {\sqrt {x^2 + a^2}}$

Also see

 * Derivative of $\cosh^{-1} \dfrac x a$


 * Derivative of $\tanh^{-1} \dfrac x a$


 * Derivative of $\operatorname{coth}^{-1} \dfrac x a$


 * Derivative of $\operatorname{sech}^{-1} \dfrac x a$


 * Derivative of $\operatorname{csch}^{-1} \dfrac x a$