Calculus AI Solver
Solve derivatives, integrals, limits, and calculus problems online with AI. Get worked steps and symbolic results.
Preview
What Can This Tool Solve?
Keptune's Calculus AI handles problems from single-variable and multivariable calculus, showing full step-by-step working. Whether you are stuck on a homework problem or need to verify your approach, type the problem in plain English or standard notation and get a detailed solution.
Supported topics:
- Limits — evaluating limits, L'Hôpital's rule, limits at infinity, one-sided limits
- Derivatives — power rule, chain rule, product/quotient rule, implicit differentiation, higher-order derivatives
- Applications of derivatives — finding critical points, local/global minima and maxima, curve sketching, related rates, linear approximation
- Optimization — maximizing or minimizing a quantity subject to a constraint
- Integrals — indefinite and definite integrals, substitution, integration by parts, partial fractions, trigonometric integrals
- Applications of integrals — area between curves, volumes of solids of revolution, arc length, average value
- Differential equations — first-order separable and linear ODEs
- Series — Taylor and Maclaurin series, convergence tests
Example Problems
| Topic | Example |
|---|---|
| Limit | Find the limit as x → 0 of (sin x)/x |
| Derivative | Differentiate f(x) = x² · e^(3x) |
| Implicit differentiation | Find dy/dx for x² + y² = 25 |
| Optimization | Find the dimensions of a rectangle with area 100 that minimizes perimeter |
| Indefinite integral | Integrate x² · ln(x) dx |
| Definite integral | Evaluate the integral from 0 to π of sin(x) dx |
| Related rates | A ladder 10 ft long leans against a wall. If the base slides away at 2 ft/s, how fast is the top sliding down when the base is 6 ft from the wall? |
Tips for Best Results
- State the variable — e.g. "differentiate with respect to x" if it could be ambiguous
- Specify the point — for tangent lines or instantaneous rates, include the x-value
- Include all constraints — for optimization problems, state both the objective (what to minimize/maximize) and the constraint
- Multi-part problems — paste the full problem with all sub-parts; the AI works through each in order
Frequently Asked Questions
Does it show step-by-step working? Yes — every solution includes a full breakdown with the rule or technique applied at each step. This is designed to help you understand the method, not just get the answer.
Can it verify my existing solution? Yes — paste your work and ask "is this correct?" or "where did I make a mistake?".
Can it handle multivariable calculus? Yes — partial derivatives, gradients, directional derivatives, double integrals, and Lagrange multipliers are all supported.
What notation should I use?
Standard notation works: x^2 for x², sqrt(x) for √x, e^x for eˣ, ln(x) for natural log. You can also write problems in plain English — e.g. "the derivative of x squared times the natural log of x".