How to use the polynomial derivative calculator
Type a polynomial f(x) and the tool collects like terms, then returns the first derivative f′(x) and the second derivative f″(x). Add an x value and it also reports f(a), the derivative value f′(a), and the tangent line y = f′(a)(x − a) + f(a) rewritten as y = mx + b.
Only one rule is used: the power rule. The derivative of xⁿ is nxⁿ⁻¹ and a constant term becomes 0, so 3x³ − 2x² + 5x − 7 differentiates to 9x² − 4x + 5. Terms of the same degree are merged automatically and terms whose coefficient becomes 0 are dropped from the printed expression.
This calculator supports polynomials only. Transcendental functions such as sin, cos, log and eˣ, terms with non-integer exponents such as √x or 1/x, and the product, quotient and chain rules are not supported. The input box accepts digits and x, ^, +, − only; anything else triggers a message. Degrees up to 12 are supported.
Coefficients may be decimals and results are printed to 6 decimal places. Because binary floating point is not exact, a coefficient is treated as zero when its absolute value is below 1e-9. Since the derivative value is exactly the slope of the tangent, you can use the tangent line output directly for rate-of-change and tangent-line problems.
Frequently asked questions
No. This calculator handles polynomials only. Trigonometric, exponential, logarithmic and composite functions are not supported.
The derivative f′(x) is an expression, while the derivative value f′(a) is a single number you get by substituting a specific x. That number equals the slope of the tangent at that point.
It expands y = f′(a)(x − a) + f(a) into y = mx + b, where m is the derivative value and b equals f(a) − f′(a)·a.