Maths & numbers
Numerical derivative workspace
Estimate first and second derivatives and compare sensitivity to the chosen step.
A clear answer. Here’s how.
Uses five-point central finite differences at X−2h, X−h, X, X+h and X+2h. Repeats the first-derivative calculation at h/2 and reports the absolute change as a sensitivity diagnostic. Requires finite function values. Very small steps amplify rounding; large steps introduce truncation error. The sensitivity value is not a certified error bound.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Expression in x
- sin(x)
- Evaluate at X
- 1
- Central difference step h
- 0.001
Example result
- First derivative estimate
- 0.540302305868
- Second derivative estimate
- -0.84147098478
- First-derivative step sensitivity
- 0.000000000000111022302463
Five-point central differences. Step sensitivity compares h and h/2; it is not a certified error bound.