cos

import std.math;
// f(x) = cos(x), f'(x) = -sin(x)
auto x = dual(0.0, 1.0);
auto result = cos(x);
assert(approxEqual(result.re, 1.0)); // cos(0) = 1
assert(approxEqual(result.du, 0.0)); // -sin(0) = 0

x = dual(PI / 2.0, 1.0);
result = cos(x);
assert(approxEqual(result.re, 0.0)); // cos(π/2) = 0
assert(approxEqual(result.du, -1.0)); // -sin(π/2) = -1

// f(x) = cos(3x), f'(x) = -3sin(3x)
x = dual(5.0, 1.0);
result = cos(3 * x);
assert(approxEqual(result.re, std.math.cos(15.0)));
assert(approxEqual(result.du, -3.0 * std.math.sin(15.0)));