Third Derivative Calculator
Compute the third derivative of standard function forms for jerk analysis.
About Third Derivative Calculator
Computes the third derivative f'''(x) using the finite difference formula: f'''(x) ≈ [f(x+2h) − 2f(x+h) + 2f(x−h) − f(x−2h)] / (2h³). In physics, the third derivative of position with respect to time is called jerk.
Formula
Third derivative
f'''(x) ≈ [f(x+2h) - 2f(x+h) + 2f(x-h) - f(x-2h)] / (2h³)
- f(x)
- The input function
- x
- Point of evaluation
- h
- Step size (≈1e-4)
Worked example
With the default values below, Third Derivative Calculator returns f'''(x) of 47.999937. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f(x)
- x^5 - 2*x^3 + x
- Evaluate at x
- 1
Results
- f'''(x)
- 47.999937
- f''(x)
- 8.000002
- f'(x)
- -0.000000
Step by step
- 1Values used
- 2Third derivative
- 3f'''(x)= 47.999937
- 4f''(x)= 8.000002
- 5f'(x)= -0.000000
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the physical meaning of the third derivative?
In kinematics, it represents jerk — the rate of change of acceleration. It's important in engineering for ride comfort analysis.
Why is a larger step size used?
Higher-order finite differences amplify numerical noise, so a slightly larger h balances truncation error against round-off error.