How to use the derivative of a polynomial at a point calculator
Differentiate ax³ + bx² + cx + d and evaluate the slope at x. Enter a, b, c, d, x in the fields above; the function value f(x), derivative f′(x), second derivative f″(x) are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “derivative”, “slope of tangent”, “rate of change”, “calculate derivative of a polynomial at a point”, “find function value f”.
Formula
Variables
- a — a
- b — b
- c — c
- d — d
- x — x
Worked example
With a = 2, b = -3, c = 1, d = 5, x = 2, the calculator gives function value f(x) ≈ 11; derivative f′(x) ≈ 13; second derivative f″(x) ≈ 18.
Frequently asked questions
What is the derivative of a polynomial at a point calculator used for?
Differentiate ax³ + bx² + cx + d and evaluate the slope at x. It helps with questions such as “derivative”, “slope of tangent”, “rate of change”.
What is the formula for the derivative of a polynomial at a point calculation?
Function value f(x) = a × x^3+b × x × x+c × x+d. Derivative f′(x) = 3 × a × x × x+2 × b × x+c. Second derivative f″(x) = 6 × a × x+2 × b. Here a is a, b is b, c is c, d is d, x is x.
What inputs do I need for the derivative of a polynomial at a point calculator?
You need a, b, c, d, x. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the derivative of a polynomial at a point calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the derivative of a polynomial at a point result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.