Enter any calculus problem — a derivative, an integral, or a limit — and our AI engine works through it one clear step at a time, so you can follow the reasoning and check your own work.
Free · Step-by-step worked solutions · Works on any device
What this calculus solver does
This calculus solver takes a single-variable calculus problem and returns a complete, step-by-step solution. Instead of just handing you a final number, it shows the rule used at each stage so you can see why the answer is what it is.
It handles the three core areas of a first calculus course:
- Derivatives — power rule, product rule, quotient rule, chain rule, and trigonometric, exponential, and logarithmic functions.
- Integrals — indefinite and definite integrals, substitution, and basic standard forms.
- Limits — direct substitution, factoring, indeterminate forms like \( \tfrac{0}{0} \), and one-sided limits.
Type your problem in plain text or build it with the equation editor. Just type your problem in plain text or build it with the equation editor — clear, editable math, your way.
Worked examples
Example 1: A derivative with the chain rule
Differentiate \( f(x) = (3x^2 + 1)^5 \).
The chain rule says: differentiate the outer function, then multiply by the derivative of the inside.
Outer function: \( u^5 \), whose derivative is \( 5u^4 \). Inside: \( u = 3x^2 + 1 \), whose derivative is \( 6x \).
$$ f'(x) = 5(3x^2 + 1)^4 \cdot 6x = 30x(3x^2 + 1)^4 $$Example 2: A definite integral
Evaluate \( \displaystyle \int_{0}^{2} (6x^2 - 4x + 5)\,dx \).
First find the antiderivative term by term using the power rule \( \int x^n\,dx = \tfrac{x^{n+1}}{n+1} \):
$$ F(x) = 2x^3 - 2x^2 + 5x $$Now apply the limits with \( F(2) - F(0) \):
$$ F(2) = 2(8) - 2(4) + 5(2) = 16 - 8 + 10 = 18 $$ $$ F(0) = 0 $$Example 3: A limit with an indeterminate form
Evaluate \( \displaystyle \lim_{x \to 3} \frac{x^2 - 9}{x - 3} \).
Substituting \( x = 3 \) gives \( \tfrac{0}{0} \), which is indeterminate, so we simplify first. Factor the numerator as a difference of squares:
$$ \frac{x^2 - 9}{x - 3} = \frac{(x - 3)(x + 3)}{x - 3} = x + 3 $$The \( (x - 3) \) factors cancel, and now substitution works:
$$ \lim_{x \to 3} (x + 3) = 3 + 3 = 6 $$Common mistake
Always add the constant \( +C \) to an indefinite integral. It is only dropped for a definite integral, where the limits cancel it out.
How to use the calculus solver
- Enter your problem. Type the function, integral, or limit, or use the equation editor for exponents, fractions, and special symbols.
- Choose what to find. Make it clear whether you want a derivative, an integral (with or without bounds), or a limit, including the value the variable approaches.
- Read the steps. Review each line, confirm the final answer, and rework any step yourself to lock in the method.
Study tip
Try the problem on paper first, then compare each line with the solver. The places where your work diverges show you exactly which rule to review.
Related step-by-step guides
- How to Find Derivatives: Rules and Examples — a tour of the power, product, and quotient rules.
- How to Solve Integrals: A Beginner’s Guide — antiderivatives and definite integrals made approachable.
- Understanding Limits in Calculus — what limits mean and how to evaluate the tricky ones.
- The Chain Rule Explained with Examples — a focused walkthrough for composite functions.
Explore more solvers
Need to handle the algebra inside your calculus work? Try our Equation Solver or Algebra Solver for the steps that come before differentiating and integrating.
