Hyperbolic

cosh,dual-method

sinh,dual-method

tanh,dual-method

acosh,dual-method

asinh,dual-method

atanh,dual-method

These functions provide the obvious hyperbolic functions. 
They respectively compute the hyperbolic cosine, sine, tangent, 
and their inverses, arc-cosine, arc-sine, arc-tangent.

Automatic differentiation is achieved by using dual numbers without
providing hand-coded gradient functions. The output value of a mathematical
function is returned with the values of its exact first derivative
(or gradient). For more details see Baydin, Pearlmutter, Radul, and Siskind
(2018) <https://jmlr.org/papers/volume18/17-468/17-468.pdf>.

Luca Sartore

dual

Automatic Differentiation with Dual Numbers

Hyperbolic function

<dl><dt>x</dt>
<dd>a dual object</dd></dl>

Arguments

Hyperbolic Functions — Hyperbolic

<dl>

<dt>x</dt>
<dd>a dual object</dd>

</dl>

Hyperbolic: Hyperbolic Functions

Description

Usage

Value

Arguments

Examples