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@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@ This is cppad-20221105 documentation. Here is a link to its current documentation .
The AD acos Function: Example and Test

# include <cppad/cppad.hpp>

bool acos(void)
{   bool ok = true;

    using CppAD::AD;
    using CppAD::NearEqual;

    // 10 times machine epsilon
    double eps = 10. * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t n  = 1;
    double x0 = 0.5;
    CPPAD_TESTVECTOR(AD<double>) x(n);
    x[0]      = x0;

    // declare independent variables and start tape recording
    CppAD::Independent(x);

    // a temporary value
    AD<double> cos_of_x0 = CppAD::cos(x[0]);

    // range space vector
    size_t m = 1;
    CPPAD_TESTVECTOR(AD<double>) y(m);
    y[0] = CppAD::acos(cos_of_x0);

    // create f: x -> y and stop tape recording
    CppAD::ADFun<double> f(x, y);

    // check value
    ok &= NearEqual(y[0] , x0,  eps, eps);

    // forward computation of first partial w.r.t. x[0]
    CPPAD_TESTVECTOR(double) dx(n);
    CPPAD_TESTVECTOR(double) dy(m);
    dx[0] = 1.;
    dy    = f.Forward(1, dx);
    ok   &= NearEqual(dy[0], 1., eps, eps);

    // reverse computation of derivative of y[0]
    CPPAD_TESTVECTOR(double)  w(m);
    CPPAD_TESTVECTOR(double) dw(n);
    w[0]  = 1.;
    dw    = f.Reverse(1, w);
    ok   &= NearEqual(dw[0], 1., eps, eps);

    // use a VecAD<Base>::reference object with acos
    CppAD::VecAD<double> v(1);
    AD<double> zero(0);
    v[zero] = cos_of_x0;
    AD<double> result = CppAD::acos(v[zero]);
    ok     &= NearEqual(result, x0, eps, eps);

    return ok;
}
Input File: example/general/acos.cpp