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Polynomial derivative
Polynomial derivative: formula, units and explained result. No account required. Processing stays in your browser.
p(x) = ax³ + bx² + cx + d; p′(x) = 3ax² + 2bx + c
Polynomials up to degree 3; shows derivative and slope at x.
How to use this calculator
- Identify the quantities and convert them to the units shown.
- Apply the formula first, then compare with the substitution and result.
- Check the assumptions and whether the order of magnitude makes sense.
Levels are approximate topic groupings, not a complete curriculum for every country. Numerical results are rounded and may lose precision for extreme or nearly singular inputs.
A practical example
Use these sample inputs to check the calculation before entering your own values.
- a
- 1
- b
- 2
- c
- 3
- d
- 4
- Point x
- 2
Result for this example
- Derivative
- 3x² + (4)x + (3)
- Slope
- 23
- p(x)
- 26