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Calculus · Differentiation

Polynomial Derivative Calculator

Differentiate polynomials up to degree five symbolically and see how the power rule transforms every term and removes the constant term.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Real-coefficient polynomials from degree one through five

Power rule

d(axⁿ)/dx = naxⁿ⁻¹

Linearity

d(f+g)/dx = f′ + g′

Constant rule

d(c)/dx = 0
Calculus · Symbolic rules

Differentiate a polynomial

Inputs and displayed decimal results use at most three decimal places. Exact internal values are retained during calculation.

d(axⁿ)/dx = naxⁿ⁻¹

Choose a degree and enter the polynomial coefficients.

Using the model

Symbols, assumptions and limitations

Interpretation notes

The supported grammar is deliberately limited to real-coefficient polynomials of degree one through five. This makes every transformation transparent and avoids implying support for unrestricted computer algebra.

Worked examples

See the method in practice

01

Cubic polynomial

For f(x) = 3x³ − 2x + 5, the power rule gives f′(x) = 9x² − 2.

02

Constant contribution

The derivative of the constant term 5 is zero because it does not change with x.

Questions

Frequently asked

Does this differentiate trigonometric functions?

Not in this reviewed version. It supports real-coefficient polynomials only.

Why limit the degree?

Degree five covers common school examples while keeping input and explanations compact on small screens.

Is the derivative exact?

Yes for the entered decimal coefficients; formatting may omit trailing zeros.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax Calculus Volume 1 — Derivatives

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology