Examples
Examples
Try the starting example
- Restricted real expression f(x)
- x^3
- Evaluation point x
- 2
- Positive central-difference step
- 0.1
- Five-point derivative estimate
- 12
- Estimate with half the step
- 12
- Absolute step-halving discrepancy
- 0
Try another scenario
- Restricted real expression f(x)
- sin(x)
- Evaluation point x
- 0
- Positive central-difference step
- 0.5
- Five-point derivative estimate
- 0.997978
- Estimate with half the step
- 0.999871
- Absolute step-halving discrepancy
- 0.001893
Calculation method
Calculation method
Five-point derivative estimate
[f(x−2h)−8f(x−h)+8f(x+h)−f(x+2h)]/(12h).
Estimate with half the step
Repeat the same five-point stencil with h/2.
Absolute step-halving discrepancy
Absolute difference between the two estimates; not a certified derivative error.
Symbols and units
- a
- Restricted real expression f(x)
- b
- Evaluation point x
- c
- Positive central-difference step
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- A fourth-order central stencil for sufficiently smooth real functions. Every sampled point must be in the finite real domain; excessively small steps can amplify roundoff. Restricted expressions allow x (and y for ODEs), pi, e, + - * / ^, and sin, cos, tan, sec, csc, cot, exp, log, sqrt, abs, sinh, cosh, tanh, sech, csch, coth. Trigonometric arguments are in radians. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
SciPy: numerical integration and ODE method references ↗
Background reading; this does not imply endorsement or independent review of SumFizz.