Calculus
Symbolic derivatives and integrals where a closed form exists, and clearly labelled numerical methods where it does not. Analytic and approximate results are never mixed up.
Derivative CalculatorDifferentiate functions symbolically — first, second and higher derivatives — with the rules used and a numerical verification.Partial Derivative CalculatorPartial and mixed partial derivatives of multivariable functions, plus the full gradient.Integral CalculatorIndefinite integrals (antiderivatives) found symbolically and verified by differentiation before they are shown.Definite Integral CalculatorEvaluate definite and improper integrals: analytically when an antiderivative exists, otherwise by adaptive quadrature.Limit CalculatorFinite, one-sided and infinite limits, including 0/0 and ∞/∞ forms, estimated numerically and confirmed symbolically when possible.Taylor Series CalculatorTaylor and Maclaurin polynomials about any point up to order 12, with coefficients and a plot against the original function.Differential Equation SolverAnalytic solutions of constant-coefficient linear ODEs of first and second order, and RK4 numerical solutions of y′ = f(x, y).Numerical Integration CalculatorApproximate integrals with the trapezoidal, midpoint and Simpson’s rules and compare them with an adaptive reference value.Numerical Differentiation CalculatorApproximate derivatives with forward, backward, central and five-point differences and compare with the symbolic value.