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Calculus AI Solver rule by rule

Paste a limit, derivative, integral or applied problem, or upload a photo. You see which rule applies at each step, with formulas in clean math notation.

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Result

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What you get on a calculus problem

  • The rule at each step

    Chain, product or quotient rule, L'Hôpital, substitution, integration by parts, the Fundamental Theorem or a series test — named exactly where it is applied.

  • Differentiated back

    Antiderivatives are checked by taking their derivative, and indefinite integrals end with + C.

  • Domain and continuity

    Restrictions, discontinuities and improper integrals are pointed out instead of skipped.

  • Word problems modeled

    Related rates, optimization, area and volume are set up in words before any computing begins.

Choosing a technique: a quick guide

For derivatives, look at how the function is built. A product such as x²·sin x needs the product rule, (fg)′ = f′g + fg′. A quotient uses (f/g)′ = (f′g − fg′) ÷ g². A function inside another, such as sin(3x²), needs the chain rule: differentiate the outside, keep the inside, then multiply by the derivative of the inside, giving cos(3x²) · 6x.

For integrals, first ask whether one part of the integrand is the derivative of another part. In ∫ 2x·cos(x²) dx, the 2x is the derivative of x², so substituting u = x² turns it into ∫ cos u du = sin(x²) + C. When the integrand multiplies two unrelated kinds of function, such as x·eˣ, integration by parts, ∫ u dv = uv − ∫ v du, is usually the tool.

For limits, try direct substitution first. Only when it gives an indeterminate form such as 0/0 or ∞/∞ do you factor, rationalize, or apply L'Hôpital's rule.

Worked example: area between y = x² and y = 2x

  • Find where they meet

    Set x² = 2x, so x(x − 2) = 0 and the curves cross at x = 0 and x = 2.

  • Decide which is on top

    Test x = 1: 2x gives 2 while x² gives 1, so y = 2x is the upper curve on this interval.

  • Integrate top minus bottom

    Area = ∫₀² (2x − x²) dx = [x² − x³/3] from 0 to 2 = 4 − 8/3 = 4/3.

  • Sanity check

    The region fits inside a 2 by 4 rectangle of area 8, and 4/3 is a modest positive slice of it, which is plausible.

How to ask a calculus question

  1. Write it clearly

    Use ^ for powers and brackets for grouping, e.g. (x^2 + 1)/(x − 3), or snap the textbook page instead.

  2. Set your course level

    High school or college — the depth of justification follows the grade you pick, and you can choose an explanation style.

  3. Read it rule by rule

    The approach names the technique, and each numbered step shows one algebraic move.

  4. Practice and follow up

    Verify the result the suggested way, try the similar problem, then ask a follow-up in AI Chat.

Frequently asked questions

Short ones, yes, with each inequality explained. Very long or multi-part proofs are where it is most likely to skip or fumble a step, so break them into smaller questions and check each one.

It cannot draw a graph. It describes the shape instead — intercepts, where the function rises or falls, concavity and asymptotes — so you can sketch it yourself.

Those free calculators give a fast result and step outline for a single expression. Use the solver when you need the reasoning explained, an applied word problem set up, or a photo read.

Calculus questions come with the Pro plans* (*fair use: up to 300 runs a day across the writing, study and code tools). Otherwise each question uses 2 credits, or 3 when you add a photo. You can see the start of an answer without signing in.

Treat the worked solution as a study aid for learning and checking. Graded work usually comes with rules about AI, so follow them and read our Academic Integrity page.

It may well be. AI can drop a sign or a factor, so differentiate back, plug in a test value, or ask a follow-up that points to the step you doubt.

Calculus companions

Stuck on a limit or an integral?

See which rule fits and why, then prove it to yourself with a practice problem.

Solve my calculus problem
  • Each rule named
  • Answers differentiated back
  • Clean math notation