Third Derivative Calculator
Compute the third derivative of standard function forms for jerk analysis.
Inputs
Enter function using x as variable.
f'''(x)
47.999937
f''(x)
8.000002
f'(x)
-0.000000
Step by step
Values used
f(x) = x^5 - 2*x^3 + x; Evaluate at x = 1
Third derivative
f'''(x) ≈ [f(x+2h) - 2f(x+h) + 2f(x-h) - f(x-2h)] / (2h³)
f'''(x)
= 47.999937
f''(x)
= 8.000002
f'(x)
= -0.000000
How it works
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)
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.