Enter the coefficients of a polynomial and instantly get its derivative, term by term, using the power rule.
Polynomial Derivative Calculator
How It’s Calculated
The power rule says d/dx(a·xⁿ) = a·n·x(n−1) — multiply the coefficient by the exponent, then reduce the exponent by 1. This calculator applies that rule to every term in your polynomial independently, since the derivative of a sum is the sum of the derivatives.
Worked Example
For f(x) = 2x³ + 5x² − 4x + 7: differentiate term by term. d/dx(2x³) = 6x². d/dx(5x²) = 10x. d/dx(−4x) = −4. d/dx(7) = 0 (constants vanish). So f'(x) = 6x² + 10x − 4.
Frequently Asked Questions
Q: Why does the constant term disappear?
A constant has no x in it — it’s really a·x⁰. Its slope is 0 everywhere, since a constant doesn’t change as x changes.
Q: Does this work for functions with sin, cos, or eˣ?
Not this tool — it’s built specifically for polynomials using the power rule. Trigonometric and exponential derivatives follow different rules covered later in Limits and Derivatives and Continuity & Differentiability.
The power rule is the foundation everything else in Limits & Derivatives and Continuity & Differentiability builds on. See how Daniel Classes teaches 1st and 2nd PUC Mathematics →