Derivative calculator (polynomials)
Differentiate polynomials with the power rule and evaluate f(x) and f'(x) at a point.
This calculator covers polynomials (power rule). Functions with sine, exponentials, fractions of x etc. are not supported.
How the calculation works
The power rule differentiates each term: d/dx (a·xⁿ) = a·n·xⁿ⁻¹. Constants vanish (derivative 0).
Example: f(x) = 3x³ − 2x² + x − 5 → f'(x) = 9x² − 4x + 1. The derivative at a point is the curve's slope there: f'(2) = 29 means at x = 2 the function rises 29 units per unit of x.
Examples
- f(x) = x² → f'(x) = 2x. At x = 3, the slope is 6.
- f(x) = 5x³ → f'(x) = 15x². The constant in f(x) = 7 has derivative 0.
Frequently asked questions
What does the derivative mean?
The instantaneous rate of change: the slope of the tangent line at that point. Where f'(x) = 0, the function has a maximum, minimum or inflection point.
Does it work beyond polynomials?
Not here — the focus is the power rule, which covers most introductory exercises. Sine, log and exponentials have their own rules.
How does the power rule work?
The exponent comes down as a multiplier, and the new exponent is the old minus 1: d/dx(xⁿ) = n·xⁿ⁻¹. E.g. x⁴ → 4x³.
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Updated on July 4, 2026 · by Rafael Rossi · Methodology & sources