Derivative Calculator with Steps: Differentiate Functions Instantly
Type any function and watch it differentiate in real time — with every rule named and explained in plain English. Solve step-by-step derivatives for your calculus homework offline or on mobile.
Derivative
How to Find Derivatives of Any Calculus Function
Mastering symbolic differentiation starts with understanding basic mathematical inputs. Follow our guided steps below to optimize your calculations.
1. Standard Notation & Inputs
To calculate derivatives accurately, always make use of explicit algebraic operators. Write 3*x instead of 3x if you encounter parsing errors. For exponents, use the carat operator: x^5. When writing trigonometric functions, always enclose the parameter in brackets, e.g., sin(4*x).
2. Understanding Basic Rules & Steps
The engine behind DerivCalc executes a series of procedural mathematical proofs. It scans the input string, parses the variables symbolically, and matches the tokens with established differentiation algorithms. By showing the exact rule names like Chain Rule, Product Rule, and Quotient Rule, this portal acts as an active digital tutor, clarifying complex steps as you study.
3. Evaluating the Derivative at a Point
Once the symbolic derivative is resolved, you can substitute any numerical parameter in the evaluation input box. This instantly computes the slope of the tangent line at that exact coordinate point (e.g., x = 2), saving you valuable time on calculus homework verification checks.
Try an example
Click any function to load it into the calculator and see the full worked solution.
The four rules that solve almost everything
Differentiation looks intimidating, but most problems come down to recognizing which of these patterns you're looking at. DerivCalc tags each one as it works.
Common derivatives
A quick reference for the standard functions. Every one of these is built into the calculator above.
| Function f(x) | Derivative f′(x) |
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Want the full walkthrough for a specific function? Browse our library of worked derivative solutions — each one explains the rule, the steps, and the mistakes to avoid.
Questions students ask
Short, honest answers about derivatives and how to use this tool.
How do I type a function?
^ for powers (x^2), * or just juxtaposition for multiplication (2x or 2*x both work), and / for division. Function names take parentheses: sin(x), ln(x), sqrt(x), e^x. The live preview shows exactly how your input was read, so you can catch a stray parenthesis before you trust the answer.Does it show the steps, or just the answer?
What's the difference between ln and log here?
ln is the natural logarithm (base e) and log is base 10. So the derivative of ln(x) is 1/x, while log(x) gives 1/(x·ln 10). If your textbook writes "log" to mean natural log, type ln instead.