โDerivative Calculator
Differentiate any function step by step โ chain, product, and quotient rules explained, with a graph of f(x) and f'(x).
Calculations run entirely in your browser using math.js for parsing, symbolic differentiation, and evaluation. No data is sent to a server.
Free Derivative Calculator With Steps
Need to find a derivative fast โ or actually understand how to get there? Our free derivative calculator with steps solves it instantly and shows every step along the way. Type in any function, choose the order of the derivative you need, and watch the chain rule, product rule, quotient rule, and power rule applied explicitly, not just summarized.
Unlike calculators that only spit out an answer, this one shows the reasoning: which rule fires at each step and how the expression simplifies down to the final result. A live graph plots your function alongside its derivative, so you can see the relationship between a curve and its slope. Non-differentiable points are detected and explained clearly instead of throwing an error.
Enter a function to get started. No sign-up, no downloads, no limits. See the About page or the FAQ for more.
About the Derivative Calculator
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.
Frequently Asked Questions
How does the derivative calculator work?
Enter a function of x, choose the derivative order, and it differentiates instantly, showing every rule applied along the way.
Is it free?
Completely free, no sign-up, downloads, or limits.
Does it show the steps, not just the answer?
Yes, each differentiation rule (power, chain, product, quotient) is shown explicitly in sequence.
Can it compute higher-order derivatives?
Yes, choose 1st through 4th derivative from the order selector.
What functions are supported?
Polynomials, trigonometric, exponential, logarithmic, and root functions, plus combinations of them via the chain/product/quotient rules.
Can I evaluate the derivative at a specific point?
Yes, enter a value of x to get the numeric slope of the tangent line at that point.
What happens at points where the function isn't differentiable?
The calculator detects these (e.g. division by zero, invalid domain) and explains why, instead of showing an error or NaN.
Does it simplify the final answer?
Yes, the derivative is simplified and combined into its most readable form.
Is my input stored anywhere?
No; everything runs in your browser and isn't stored or sent anywhere.
Does it work on mobile?
Yes, fully responsive, including the graph and step-by-step panel.