Search Ctrl K
Home / Tools
THE FEUTEX TOOLKIT

Five-Point First Derivative

Estimate a first derivative with a fourth-order centered stencil.

Math workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaDerivative = (ym2-8*ym1+8*yp1-yp2)/(12*h)
Sources and model references

Made for real tasks

  • Estimate a first derivative with a fourth-order centered stencil.
Explore step-by-step workflows →

Worked example

Inputs

Sample spacing
0.1 number
f(x−2h)
0.64 number
f(x−h)
0.81 number
f(x+h)
1.21 number
f(x+2h)
1.44 number

Expected results

Derivative
2 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter sample spacing, f(x−2h), f(x−h), f(x+h), f(x+2h).
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "h": 0.1,
  "ym2": 0.64,
  "ym1": 0.81,
  "yp1": 1.21,
  "yp2": 1.44
}

Accuracy and scope

Requires smooth data at equal spacing. Measurement noise and floating-point cancellation can dominate at small h.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.