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.

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.

For other maths topics, see our algebra solver, geometry solver, or statistics solver.