Derivative Power Rule Calculator
Differentiate a polynomial term by term.
Enter your values
ⓘ Live results
Results
- Derivative
- 6x^2 + -6x + 5
- Derivative at x
- 17
- Original degree
- 3
Quick answer
The power rule states d/dx[ax^n] = n*a*x^(n-1); apply it term by term to differentiate a polynomial.
d/dx[ax^n] = n*a*x^(n-1)
How to use the Derivative Power Rule Calculator
- 1Enter the coefficients of your cubic polynomial.
- 2Each term's exponent is multiplied by its coefficient and the exponent drops by one.
- 3Optionally evaluate the resulting derivative at a specific x.
Worked example
Using the values the calculator loads with:
Inputs
- Coefficient of x^32
- Coefficient of x^2-3
- Coefficient of x5
- Constant7
- Evaluate derivative at x (optional)2
Results
- Derivative6x^2 + -6x + 5
- Derivative at x17
- Original degree3
Frequently asked questions
What if my polynomial is lower degree?
Set the higher-degree coefficients to 0.
Does this handle non-polynomial functions?
No — for trig, exponential or log derivatives, use the appropriate rule directly.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.