Use this numerical method to approximate a derivative or definite integral from a callable expression and explicit step or interval settings.

Coefficients

Polynomial coefficients where index i holds the coefficient of x^i.

Point

Evaluation point of the derivatives.

Step size

Finite-difference step; positive powers of two (e.g. 0.0078125) avoid representation error.

Approximate first and second derivatives of a polynomial via central finite differences. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

derivative

Central-difference estimate of f'(x).

secondDerivative

Central second-difference estimate of f''(x).

• Numerical differentiation and integration introduce truncation and floating-point error. Discontinuities, singularities, oscillation, cancellation, or an unsuitable step size can make a plausible-looking result inaccurate.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Repeat the calculation with a finer resolution and compare the change. Use symbolic calculus or an adaptive high-precision method when an exact result or controlled error bound is required.

• Simpson Integration Calculator

  Approximate a definite integral from evenly spaced samples over [xMin, xMax] using composite Simpson's rule (odd sample count required).

• Trapezoidal Integration Calculator

  Approximate a definite integral from evenly spaced samples over [xMin, xMax] using the composite trapezoidal rule.

• Subtract Two Numbers Calculator

  Subtract the second finite number from the first.