How to Differentiate Functions Using Math.js? - Coding

Differentiation is a fundamental concept in calculus, used extensively in mathematics, physics, engineering, and many other fields. While traditional methods of calculus involve manual calculations, modern computing tools like math.js can simplify this process significantly. Math.js is a powerful, open-source library for mathematics that runs in JavaScript and can handle a wide range of mathematical operations, including differentiation.

These are the following approaches we can use for differentiating using math.js:

Table of Content

Using NPM
Using CDN

Using NPM

To differentiate an expression using math.js with npm, first, install the library with ‘npm install mathjs’ . Then, use ‘ math.derivative (expression, variable)’ to compute the derivative. Differentiation in math.js is straightforward. The library provides a derivative function to compute the derivative of a given expression.

Install required library:

npm install mathjs

Then, include it in your JavaScript file:

const math = require('mathjs');

Example: Differentiating a Trigonometric Function, Consider the trigonometric function g(x)=sin(x).

JavaScript

const math = require('mathjs');

// Define the expression
const expression = 'sin(x)';

// Differentiate the expression with respect to x
const derivative = math.derivative(expression, 'x');

console.log(`The derivative of ${expression}
     is ${derivative.toString()}`);

Output:

The derivative of sin(x) is cos(x)

Using CDN

To differentiate an expression using math.js with a CDN, include the library in your HTML with ‘<script src=”https://cdnjs.cloudflare.com/ajax/libs/mathjs/11.0.0/math.min.js”></script>’ . Then use ‘ math.derivative(expression, variable)‘ in your JavaScript code to compute the derivative.

Add these script in your HTML file:

<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/10.0.0/math.js"></script>
<script>
  // Your code here
</script>

Example: Differentiating a Polynomial. Consider the polynomial f(x)= 3x^2 + 2x + 1.

HTML

<!DOCTYPE html>
<html lang="en">

<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width,
                  initial-scale=1.0">

</head>

<body>
    <h1 id="header"></h1>
    <script src=
"https://cdnjs.cloudflare.com/ajax/libs/mathjs/10.0.0/math.js"></script>
    <script>
        // Define the expression
        const expression = '3x^2 + 2x + 1';

        // Differentiate the expression with respect to x
        const derivative = math.derivative(expression, 'x');

        console.log(`The derivative of ${expression}
                    is ${derivative.toString()}`);

    </script>
</body>

</html>

Output:

The derivative of 3x^2 + 2x + 1 is 6 * x + 2

Reffered: https://www.geeksforgeeks.org

JavaScript

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