About the Derivative Calculator
Symbolically differentiates any function of x, with rule-by-rule steps, higher-order derivatives, and a graph.
What it is
Type any function of x using standard notation and the calculator parses it, differentiates it symbolically using math.js, and simplifies the result. A step panel explains which differentiation rule (power, chain, product, quotient) applies to the top-level structure of your expression.
Features
Rule-by-rule steps
Identifies sum, product, quotient, power, and chain rule applications with the actual sub-expressions.
Higher-order derivatives
Compute the 1st through 4th derivative of any function.
Point evaluation
Evaluate the derivative at any x = a to get the numeric slope of the tangent line.
Graph of f(x) and f'(x)
A live chart plots the function and its derivative together over [-10, 10].
Non-differentiable detection
Points where evaluation fails (division by zero, domain errors) are flagged clearly rather than showing NaN.
Simplified output
The final derivative is algebraically simplified for readability.
How it works
The function is parsed into an expression tree using math.js. Symbolic differentiation is performed with math.derivative(), which is repeated for higher orders, and the result is simplified with math.simplify(). The step panel additionally walks the top level of the original expression tree to describe which classical differentiation rule applies.