Struct ImplicitDifferentiation 

pub struct ImplicitDifferentiation;

Implicit differentiation operations

Implementations

impl ImplicitDifferentiation

pub fn compute( equation: &Expression, independent_var: Symbol, dependent_var: Symbol, ) -> Expression

Compute dy/dx for implicitly defined function F(x,y) = 0

Uses the formula: dy/dx = -∂F/∂x / ∂F/∂y

Examples

use mathhook_core::{expr, symbol};
use mathhook_core::calculus::derivatives::ImplicitDifferentiation;

let x = symbol!(x);
let y = symbol!(y);
// For x² + y² = 1 (circle)
let equation = expr!((x^2) + (y^2));
let dy_dx = ImplicitDifferentiation::compute(&equation, x, y);

pub fn higher_order( equation: &Expression, independent_var: Symbol, dependent_var: Symbol, order: u32, ) -> Expression

Compute higher-order implicit derivatives

Examples

use mathhook_core::{expr, symbol};
use mathhook_core::calculus::derivatives::ImplicitDifferentiation;

let x = symbol!(x);
let y = symbol!(y);
let equation = expr!((x^2) + (y^2));
let d2y_dx2 = ImplicitDifferentiation::higher_order(&equation, x, y, 2);

pub fn multiple_variables( equation: &Expression, independent_vars: Vec<Symbol>, dependent_var: &Symbol, ) -> Vec<Expression>

Handle multiple implicit variables

Examples

use mathhook_core::calculus::derivatives::Derivative;
use mathhook_core::{expr, symbol, Expression};
use mathhook_core::calculus::derivatives::ImplicitDifferentiation;

let x = symbol!(x);
let y = symbol!(y);
let z = symbol!(z);
// For F(x,y,z) = 0, compute ∂z/∂x and ∂z/∂y
let equation = Expression::add(vec![expr!(x), expr!(y), expr!(z)]);
let partials = ImplicitDifferentiation::multiple_variables(
    &equation,
    vec![x, y],
    &z
);