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Formula verified · Deterministic calculation

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

Trend

2.515.63
2.617.58
2.719.68
2.821.95
2.924.39
327
Methodology

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

Sources
  • CalcuMint deterministic numerical-calculus engine
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. Technical calculation version: 1.

  • 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.