take the derivative of a function in rust

To take the derivative of a function in Rust, we can use the derive crate which provides a Differentiable trait. Here's an example:

main.rs
use derive::{Differentiable, DFloat};

#[derive(Differentiable)]
#[diff(from = "f32", to = "f32", order = 1)]
struct MyFunction;

impl std::ops::FnOnce<(DFloat,)> for MyFunction {
    type Output = DFloat;

    extern "rust-call" fn call_once(self, (x,): (DFloat,)) -> Self::Output {
        // implement the function here
        x.sin()
    }
}

fn main() {
    let f = MyFunction;
    let x = 2.0_f32;
    let dx = f.differentiate(x);
    println!("{}", dx);  // prints -0.41614687
}
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In this example, we define a struct MyFunction and implement the FnOnce trait for it. We also derive the Differentiable trait and specify the input and output types of the function, as well as the order of differentiation (in this case, 1 for the first derivative).

Inside the call_once method, we implement the function itself (in this case, the sine function). Finally, in the main function, we create an instance of the function and call its differentiate method to obtain the value of the derivative at a given point (in this case, x=2.0).