Derivative Calculator (Polynomials)
Differentiate any polynomial in x with the power rule. Enter something like 3x^2 - 5x + 2 to get f'(x), term-by-term working, and a graph of f and f'.
About this calculator
Enter a single-variable polynomial in x using ^ for powers, e.g. 3x^2 - 5x + 2. Coefficients may be decimals; powers must be integers ≥ 0. The calculator differentiates each term with the power rule d/dx(a·xⁿ) = a·n·xⁿ⁻¹ and drops constant terms.
How polynomial differentiation works
The derivative measures the instantaneous rate of change of a function. For a polynomial you differentiate term by term using the power rule: the derivative of a·xⁿ is a·n·xⁿ⁻¹. Multiply the coefficient by the exponent, then lower the exponent by one. A constant term (power 0) has a derivative of 0, because a horizontal line has zero slope. Adding the differentiated terms back together gives f'(x), whose graph shows the slope of f at every point.