Named calculus rules
Power, sum, product, quotient, chain and supported integration or limit methods are identified when they are used.
Step-by-step calculus · Every move explained
Step by Step Calculus Calculator. See why every move works.
Enter a derivative, integral or limit and follow a readable sequence of named rules, intermediate expressions and checks instead of jumping straight to an answer.
Live solution theater
Follow the glow. Each move has a reason.
Your expressionDerivative solver
x^3 + 2x
Result preview
3 · x^2 + 2
Built around your question
A calculus calculator should show the work, not hide it
A step by step calculus calculator is most useful when the final expression is only part of the assignment. CalculusMate keeps the route to that expression visible, so you can see where a power changes, why a factor stays in place or when a limit needs simplification before substitution.
Each supported solution begins by reading the mathematical structure. The solver then applies deterministic rules in order and preserves the intermediate forms. This makes it easier to compare the work with your own notes and identify the first step where your approach changed.
The animated view is a learning aid, not a replacement for the mathematics. You can pause it, replay it or open an individual step. If the current engine cannot support a transformation reliably, the page reports that limit rather than constructing a convincing-looking answer.
Intermediate expressions
The expression after each transformation remains visible, making the reasoning easier to audit.
Deterministic answers
Core calculation is handled by the rule engine; optional AI language cannot replace the mathematical result.
Replayable explanations
Pause, replay or select a step to study a difficult transition at your own pace.
A visible calculation path
How to use the step by step calculus calculator
Start with the type of calculation, then describe the expression with ordinary keyboard notation. Task-specific fields appear only when they are needed, such as bounds for a definite integral or a direction for a one-sided limit.
- 01
Choose the calculus task
Select derivative, integral or limit so the workspace can show the controls that matter for that problem.
- 02
Enter standard math notation
Use ^ for powers and parentheses for functions such as sin(x), log(x) and exp(x). The parser rejects unrecognized input instead of guessing.
- 03
Follow each named rule
The solver keeps intermediate expressions visible and identifies the rule responsible for each supported transformation.
- 04
Check the final result
When an independent deterministic check is available, the answer receives a Verified label. Unsupported work is marked clearly.
Problems you can try
Three examples that reveal different kinds of steps
These examples show why a useful worked solution needs more than a final line. Load a similar expression in the calculator above and compare the rule sequence.
Derivative
d/dx [sin(x^2)]
The outer sine and inner square require a chain-rule sequence, so both the selected rule and the inner derivative matter.
Integral
∫ (3x^2 + 4x) dx
The integral separates into terms, restores each power and includes the integration constant for an indefinite result.
Limit
lim x→1 (x^2−1)/(x−1)
Direct substitution first exposes 0/0; factoring and cancellation make the final substitution meaningful.
What the step-by-step output can and cannot prove
A clear sequence helps you inspect a solution, but you should still check domain restrictions, assignment conventions and any assumptions required by your course. CalculusMate marks supported deterministic work as Verified and labels unsupported expressions instead of treating fluent text as proof.
FAQ
Step-by-step calculator questions
Does the calculator show every algebra step?+
It shows the ordered calculus transformations supported by the current rule engine. Very small algebra simplifications may be grouped into one readable step.
Can I use it for derivatives, integrals and limits?+
Yes. Choose a mode in the tool and provide the relevant variable, bounds, approach value or direction.
Are the explanations generated by AI?+
The mathematical answer and rule path come from the deterministic solver. Optional AI can only explain an already computed solution in plainer language.
What does Verified mean?+
It means the supported result passed an independent deterministic check before display. It does not mean every possible expression is supported.
Ready when you are
Turn the next answer into a sequence you can inspect
Use the step by step calculus calculator when you need to understand the path, review a rule or locate a mistake—not only copy the last line.