AI Calculus Solver

Calculus Topics We Solve

Differentiation

Our solver handles differentiation from first principles, the chain rule, product rule, quotient rule, implicit differentiation, parametric differentiation, and logarithmic differentiation. For each problem, the solver identifies which rule or combination of rules is needed and shows the application step-by-step. It correctly handles composite functions, trigonometric derivatives, exponential and logarithmic derivatives, and inverse trigonometric functions.

At GCSE level, differentiation is introduced in its simplest form: finding the gradient of a curve at a point and determining turning points. Our solver provides solutions appropriate to this level. At A-Level, the solver uses the full range of differentiation techniques and correctly applies them to optimisation problems, related rates of change, and curve sketching questions.

Integration

Integration by recognition, substitution, parts, partial fractions, and trigonometric identities. The solver recognises the integral form and selects the most efficient technique. For definite integrals, it shows the evaluation at both limits with proper notation. It handles improper integrals, area between curves, volumes of revolution, and the trapezium rule for numerical integration.

Differential Equations

Separable differential equations, first-order linear equations with integrating factors, second-order homogeneous and non-homogeneous equations, and simple harmonic motion. The solver classifies the equation type, applies the appropriate method, and finds both the general and particular solutions when initial conditions are given. Working is shown for finding complementary functions and particular integrals.

Limits & Continuity

Evaluating limits using algebraic manipulation, L'Hopital's rule, squeeze theorem, and standard limits. The solver identifies indeterminate forms and applies the correct technique. It also handles continuity analysis, finding points of discontinuity, and determining whether limits exist at boundary points.

University-Level Calculus

Beyond A-Level, our solver handles multivariable calculus (partial derivatives, gradient, divergence, curl), vector calculus, line and surface integrals, Green's theorem, Stokes' theorem, and the divergence theorem. These topics are covered in first and second year university mathematics courses across the UK. The working out follows the notation and conventions used in standard UK university textbooks.

Why Our Calculus Solver Is Different

Most online calculus solvers simply provide the final answer or show a single solution method. Our solver is designed to teach. It identifies the most elegant approach to each problem, explains why that method was chosen over alternatives, and shows every intermediate step that an examiner would expect to see in a complete solution. This pedagogical approach helps you develop genuine mathematical understanding rather than simply copying answers.

The solver also handles questions where calculus is combined with other mathematical areas, such as using differentiation to find the equation of a tangent at a given point (combining calculus with coordinate geometry), or using integration to find the area under a curve bounded by algebraic conditions. These cross-topic questions are common in A-Level examinations and require fluency across multiple areas of mathematics.

For other maths topics, see our algebra solver, geometry solver, or statistics solver. For GCSE-level problems, visit our GCSE maths solver. For a complete A-Level overview, see the A-Level maths solver. To compare solvers, visit best AI maths solver.