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Certified calculator · Version 1

Derivative Calculator

Enter a supported expression in x and the point where you want its derivative. CalcuMint parses the expression with its allowlisted math engine and applies refined symmetric differences.

Derivative12.0000000003

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Result methodology

A restricted deterministic expression parser feeds Richardson-refined central differences. The chart uses the same parsed expression.

Solution steps
  1. Parse f(x) = x^3
  2. Evaluate a refined central-difference derivative around x = 2
  3. f′(2) ≈ 12.00000000028264

How this calculator works

The engine evaluates central differences at progressively smaller steps and applies Richardson refinement to reduce leading truncation error.

Formula

f′(x) ≈ Richardson-refined central differences

Estimates the derivative of a supported expression at a point using symmetric finite differences and refinement.

Worked example

Derivative of x³ at 2 is a verified test case used by the calculation engine.

Assumptions and limitations

  • This is a numerical derivative, not symbolic differentiation.
  • The expression must be finite in a neighborhood of the evaluation point.
  • Supported functions include sin, cos, tan, exp, ln, log, sqrt and abs.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

  • CalcuMint deterministic numerical-calculus engine — Versioned central-difference derivative with Richardson refinement.

Frequently asked questions

Does this return a symbolic derivative?

No. It estimates the derivative value at the requested point using the certified numerical engine.

Can I enter arbitrary JavaScript?

No. Expressions use a restricted mathematical grammar and allowlisted functions.

Related calculators

Integral CalculatorCompute a finite definite integral with adaptive numerical refinement.Limit CalculatorEstimate finite one-sided or two-sided limits with convergence checks.