Derivative of Real Area Hyperbolic Sine of x over a/Corollary 1

Theorem

 * $\map {\dfrac \d {\d x} } {\ln \size {x + \sqrt {x^2 + a^2} } } = \dfrac 1 {\sqrt {x^2 + a^2} }$

Proof
We have that $\sqrt {x^2 + a^2} > x$ for all $x$.

Thus:

and the result follows.