Arcsinh

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The $\mathrm{arcsinh}$ function is the inverse function of the hyperbolic sine function defined by $$\mathrm{arcsinh}(z)=\log\left(z+\sqrt{1+z^2}\right).$$

Properties

Theorem: The following formula holds: $$\dfrac{d}{dz} \mathrm{arcsinh}(z) = \dfrac{1}{\sqrt{1+z^2}}.$$

Proof:

References

Abramowitz&Stegun

<center>Inverse hyperbolic trigonometric functions
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