Use 'x' as the variable. Supported operators: +, -, *, /, ^ (power), and standard functions like sin(x), cos(x), exp(x), log(x), sqrt(x).
function calculateInstantaneousRateOfChange() {
var functionString = document.getElementById("functionInput").value;
var pointString = document.getElementById("pointInput").value;
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
// Validate inputs
if (!functionString || !pointString) {
resultDiv.innerHTML = "Please enter both the function and the point.";
return;
}
var pointX = parseFloat(pointString);
if (isNaN(pointX)) {
resultDiv.innerHTML = "The point 'x' must be a valid number.";
return;
}
// — JavaScript Math Library for Symbolic Differentiation —
// This is a simplified symbolic differentiation. For complex functions or robustness,
// a dedicated math library like 'math.js' or a custom parser would be needed.
// This implementation will attempt basic differentiation for common polynomials and trig functions.
var derivativeString = "";
try {
// Basic polynomial differentiation: ax^n -> n*ax^(n-1)
// This is a VERY simplified parser. It won't handle complex nested functions or orders of operations perfectly.
// A more robust solution would involve abstract syntax trees (AST).
// Simple term-by-term differentiation
var terms = functionString.replace(/\s+/g, ").split(/([\+\-])/); // Split by + or – but keep delimiters
var processedTerms = [];
var currentSign = '+';
for (var i = 0; i < terms.length; i++) {
var term = terms[i];
if (term === '+' || term === '-') {
currentSign = term;
continue;
}
if (term === '') continue;
var signedTerm = currentSign + term;
var diffTerm = "";
// Handle constants
if (!signedTerm.includes('x')) {
diffTerm = "0"; // Derivative of a constant is 0
}
// Handle 'x'
else if (signedTerm === 'x' || signedTerm === '+x') {
diffTerm = "1";
} else if (signedTerm === '-x') {
diffTerm = "-1";
}
// Handle x^n
else if (signedTerm.includes('^')) {
var parts = signedTerm.split('^');
var coefficientPart = parts[0].replace('x', '');
var exponentPart = parseInt(parts[1]);
var coefficient = 1;
if (coefficientPart === '' || coefficientPart === '+') coefficient = 1;
else if (coefficientPart === '-') coefficient = -1;
else coefficient = parseFloat(coefficientPart);
if (isNaN(coefficient) || isNaN(exponentPart)) throw new Error("Invalid exponent format");
var newCoefficient = coefficient * exponentPart;
var newExponent = exponentPart – 1;
if (newExponent === 0) {
diffTerm = (newCoefficient === 1 ? "" : (newCoefficient === -1 ? "-" : newCoefficient.toString()));
} else if (newExponent === 1) {
diffTerm = (newCoefficient === 1 ? "x" : (newCoefficient === -1 ? "-x" : newCoefficient.toString() + "x"));
} else {
diffTerm = newCoefficient.toString() + "x^" + newExponent.toString();
}
}
// Handle terms like 5x (linear)
else if (signedTerm.includes('x') && !signedTerm.includes('^')) {
var coefficientPart = signedTerm.replace('x', '');
var coefficient = 1;
if (coefficientPart === '' || coefficientPart === '+') coefficient = 1;
else if (coefficientPart === '-') coefficient = -1;
else coefficient = parseFloat(coefficientPart);
if (isNaN(coefficient)) throw new Error("Invalid linear coefficient");
diffTerm = coefficient.toString();
}
// Basic function handling (very limited)
else if (signedTerm.startsWith('sin(x)')) {
diffTerm = signedTerm.replace('sin(x)', 'cos(x)');
} else if (signedTerm.startsWith('cos(x)')) {
diffTerm = "-" + signedTerm.replace('cos(x)', 'sin(x)');
} else if (signedTerm.startsWith('exp(x)')) {
diffTerm = signedTerm; // exp'(x) = exp(x)
} else if (signedTerm.startsWith('log(x)')) {
diffTerm = signedTerm.replace('log(x)', '1/x');
} else if (signedTerm.startsWith('sqrt(x)')) {
diffTerm = signedTerm.replace('sqrt(x)', '1/(2*sqrt(x))');
} else {
// If we can't parse it, leave it as is and try to evaluate, or warn.
// For this simplified calculator, we'll assume valid inputs or var eval() handle it if possible.
// A truly robust solution needs a proper parser.
throw new Error("Unsupported function format or complexity.");
}
// Re-apply sign and remove leading '+' if it exists
if (diffTerm !== "0") {
if (signedTerm.startsWith('-') && !diffTerm.startsWith('-')) {
processedTerms.push("-" + diffTerm);
} else if (signedTerm.startsWith('+') && diffTerm.startsWith('-')) {
processedTerms.push(diffTerm);
} else if (signedTerm.startsWith('+') && !diffTerm.startsWith('-')) {
processedTerms.push(diffTerm);
} else if (signedTerm.startsWith('-') && diffTerm.startsWith('-')) {
processedTerms.push(diffTerm.substring(1)); // Remove double negative
} else {
processedTerms.push(diffTerm);
}
}
}
derivativeString = processedTerms.join(" + ").replace(/\+\s*\-/g, '- ').replace(/\-\s*\-/g, '+ ').replace(/^\+\s*/, '');
if (derivativeString === "") { // If original function was a constant
derivativeString = "0";
}
// Clean up derivative string (remove unnecessary '+' signs, handle cases like '1x')
derivativeString = derivativeString.replace(/1x/g, 'x').replace(/(\+|^)\s*-/g, '-').replace(/-\s*-/g, '+').replace(/\+\s*\+/g, '+');
derivativeString = derivativeString.trim();
} catch (e) {
resultDiv.innerHTML = "Could not parse or differentiate the function. Please check syntax. Error: " + e.message + "";
return;
}
// — Evaluate the derivative at the given point —
var derivativeValue = NaN;
try {
// Replace 'x' with the point value in the derivative string and evaluate
var expressionToEvaluate = derivativeString.replace(/x/g, '(' + pointX.toString() + ')');
// Use a safe evaluation mechanism. eval() is dangerous if functionString is user-controlled from an untrusted source.
// For a calculator meant for personal use or within a controlled environment, it can be acceptable.
// A more secure approach would involve a dedicated expression parser.
// We'll simulate basic math functions that might be in the derivative string.
var safeEval = function(expr) {
// Replace common math functions with their JS equivalents
expr = expr.replace(/sin\(/g, 'Math.sin(');
expr = expr.replace(/cos\(/g, 'Math.cos(');
expr = expr.replace(/exp\(/g, 'Math.exp(');
expr = expr.replace(/log\(/g, 'Math.log(');
expr = expr.replace(/sqrt\(/g, 'Math.sqrt(');
expr = expr.replace(/\^/g, '**'); // Replace power operator for modern JS eval
// Ensure no 'x' is left, which indicates a parsing failure
if (expr.includes('x')) {
throw new Error("Unresolved 'x' in expression.");
}
return Function('"use strict";return (' + expr + ')')();
};
derivativeValue = safeEval(expressionToEvaluate);
} catch (e) {
resultDiv.innerHTML = "Could not evaluate the derivative at x = " + pointX + ". Please check function syntax and point value. Error: " + e.message + "";
return;
}
if (isNaN(derivativeValue)) {
resultDiv.innerHTML = "Calculation resulted in an undefined value. Check the function and point.";
return;
}
resultDiv.innerHTML = "