Derivative Calculator with Step-by-Step Solutions
This derivative calculator finds the derivative of any function of x and shows the full working, not just the answer. Type a function such as x^3 - 3x^2 + 2x, choose the order you need, and get the result rendered in clean mathematical notation alongside a step-by-step solution.
It handles polynomials, trigonometric, inverse trig, exponential, logarithmic, square-root and absolute-value functions, and applies the power, product, quotient and chain rules automatically. It is built for students checking calculus homework, teachers preparing examples, and anyone who needs a fast, exact derivative.
How to Use the Derivative Calculator
Enter your function
Type the function in the f(x) = field using x as the variable. Use ^ for powers, * for multiplication (or write 2x directly), / for division, and parentheses to group terms.
Choose the derivative order
Pick 1st, 2nd or 3rd, or select nth and type a custom order. Any order from 1 to 10 is supported for higher-order derivatives.
Calculate the derivative
Click Calculate Derivative or press Enter. The result appears as a formula plus a numbered step-by-step solution showing each differentiation.
Copy or explore more
Use the Copy button to copy the result, open Examples for ready-made functions to try, or tap the ? icon for syntax help.
Features
Differentiation Rules
Automatically applies the power, product, quotient and chain rules so composite expressions differentiate correctly.
Supported Functions
Differentiate trigonometric, inverse trig, exponential, logarithmic, square-root and absolute-value functions, plus polynomials.
Higher-Order Derivatives
Compute the 1st, 2nd, 3rd or any nth derivative up to the 10th, with every intermediate step shown.
Step-by-Step Solutions
See the original function and each successive derivative laid out as numbered steps, so you can follow the full process.
Clean Math Notation
Results are rendered as properly formatted mathematical formulas, making fractions, powers and roots easy to read.
Examples & Syntax Help
Load one-tap example functions and open a syntax reference covering operators, functions and constants.
Frequently Asked Questions
What functions can this derivative calculator differentiate?
It differentiates polynomials, trigonometric functions (sin, cos, tan, cot, sec, csc), inverse trig functions (arcsin, arccos, arctan), exponential functions (ex, ax), logarithmic functions (ln, log), square roots and absolute values. Composite functions are handled with the chain rule.
How do I enter my function?
Use standard notation with x as the variable. Write ^ for powers (x^3), * for multiplication (2*x or just 2x), and parentheses for grouping — for example x^3 + 2*x^2 - 5*x + 1 or sin(x)*cos(x). The constants e and pi are also recognized.
Does it show step-by-step solutions?
Yes. Every calculation lists the original function followed by each derivative as a numbered step, so you can see how the rules are applied rather than only the final answer.
Can it compute second and higher-order derivatives?
Yes. Choose 1st, 2nd or 3rd, or select nth and enter any order up to the 10th. The solution shows each successive derivative on the way to the order you requested.
Which differentiation rules does it use?
It applies the power rule, product rule, quotient rule and chain rule automatically, along with the standard derivatives of trigonometric, exponential and logarithmic functions, so you do not have to combine them by hand.
Why does my result look different from what I expected?
The calculator simplifies results automatically — for example x/x becomes 1 and 0·x becomes 0. The answer may be written differently but is mathematically equivalent to the form you had in mind.
How accurate are the results?
It performs symbolic differentiation, applying the rules exactly as you would by hand. The results are mathematically exact, not numerical approximations.
Is my data saved or sent to a server?
No. All calculations run in your browser. Your functions and results are never uploaded to a server or stored anywhere.
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