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Calculus

Derivatives, integrals, limits, and series — exact symbolic answers with every rule shown. Single-variable and multivariable. Type naturally.

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What Zeretis can solve

Zeretis covers single-variable and multivariable calculus. All results are exact — integrals return symbolic antiderivatives, not numerical estimates, and limits are evaluated algebraically where possible.

Derivatives

Any function, any order. Product rule, quotient rule, chain rule, implicit differentiation.

Indefinite integrals

Symbolic antiderivatives — u-substitution, integration by parts, trigonometric substitution.

Definite integrals

Exact evaluated results. Area under curves, improper integrals with convergence checking.

Limits

One-sided and two-sided limits, L'Hôpital's rule, limits at infinity.

Taylor & Maclaurin series

Series expansions to any order around any point.

Multivariable calculus

Partial derivatives, gradients, directional derivatives, multiple integrals.

How to type calculus problems

Derivative — plain English

differentiate x cubed sin(x)

→ 3x² sin(x) + x³ cos(x) (product rule applied)

Definite integral

integrate sin(x) from 0 to pi

→ 2 (exact)

Indefinite integral

integral of x^2 * e^x dx

→ e^x(x² − 2x + 2) + C

Limit

limit of (sin x) / x as x approaches 0

→ 1

Partial derivative

partial derivative of x^2 * y + y^3 with respect to y

→ x² + 3y²

Taylor series

Taylor series of e^x around 0 to order 5

→ 1 + x + x²/2! + x³/3! + x⁴/4! + x⁵/5!

Best practices

For higher-order derivatives, say "second derivative of..." or "d²y/dx²"
For implicit differentiation, specify "differentiate implicitly: x² + y² = 25"
For integration by parts problems, just enter the integral — the solver chooses the method automatically
Trigonometric integrals like ∫sin²(x)dx are handled — no need to supply the identity manually
For improper integrals, the solver checks convergence and tells you if the integral diverges
Multivariable: specify the variable — "partial derivative with respect to x" or "∂f/∂x"

📐Algebra 🔀Differential Equations 🔢Linear Algebra ∑Series & Sequences 📏Trigonometry

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