ClarityHow to use this tool
- Enter polynomial coefficients, evaluate derivative at x.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
The method, explained
For each term a×x^k, differentiate to k×a×x^(k−1). Drop the constant term and evaluate the resulting polynomial using Horner’s method.
Using polynomial coefficients = 3, 0, -2, 5, evaluate derivative at x = 2, the result is 34. Change these example inputs to match your task; use the method above to check each step.
Understanding your result
The numerical result is the derivative at your selected x, which is the instantaneous slope of the polynomial graph there. The coefficient list describes the full derivative.
What to keep in mind
Polynomial coefficients only; does not parse symbolic expressions, logarithms or trigonometric functions. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.
Common questions
Is the result a slope?
The numerical result is the derivative at your selected x, which is the instantaneous slope of the polynomial graph there. The coefficient list describes the full derivative.
How can I check the result?
For each term a×x^k, differentiate to k×a×x^(k−1). Drop the constant term and evaluate the resulting polynomial using Horner’s method. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.
Methodology maintained by ClarityKit. How these tools are built and checked.