Tutorial

Differentiate A Scalar Function

Use diff to compute the derivative of a scalar function.

let d = @autodiff.diff(fn(x) { x * x }, 3.0)

The result is 6.0.

Keep Value And Derivative

Use value_and_diff when both outputs are needed.

let (value, derivative) = @autodiff.value_and_diff(
  fn(x) { x * x * x },
  2.0,
)

The value is 8.0 and the derivative is 12.0.

Constants And Variables

Dual::constant(x) has zero tangent. Dual::variable(x) has unit tangent.

let c = @autodiff.Dual::constant(5.0)
let x = @autodiff.Dual::variable(2.0)

Constants differentiate to zero. The identity variable differentiates to one.

Elementary Functions

Elementary methods can be used when the base scalar supports the corresponding Luna Flow arithmetic trait.

let d = @autodiff.diff(fn(x) { x.sin() }, 0.5)

The derivative is cos(0.5).

Checked Division

Use DivChecked::div_checked when division failure must be returned as data. The operation reuses ArithmeticError and ArithmeticContext from Luna-Flow/arithmetic.

Next Steps

Use the integration tutorial for gradients, Jacobians, and polynomial derivative-at-a-point helpers:

• ../integration/tutorial.md