Derivative Power Rule Calculator
Differentiate a polynomial term by term.
Enter your values
Enter the coefficient of x^3 you are working with.
Enter the coefficient of x^2 you are working with.
Enter the coefficient of x you are working with.
Enter the constant you are working with.
Enter the evaluate derivative at x (optional) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Differentiate a polynomial term by term. |
|---|---|
| Category | Math |
| Inputs needed | Coefficient of x^3, Coefficient of x^2, Coefficient of x, Constant, Evaluate derivative at x (optional) |
| Main output | Derivative |
| Formula | d/dx[ax^n] = n*a*x^(n-1) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Coefficient of x^3
- Enter the coefficient of x^3 you are working with.
- Coefficient of x^2
- Enter the coefficient of x^2 you are working with.
- Coefficient of x
- Enter the coefficient of x you are working with.
- Constant
- Enter the constant you are working with.
- Evaluate derivative at x (optional)
- Enter the evaluate derivative at x (optional) you are working with.
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.
What do I need to enter into the Derivative Power Rule Calculator?
Just 5 values: coefficient of x^3, coefficient of x^2, coefficient of x, constant, evaluate derivative at x (optional). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Derivative Power Rule Calculator work out the answer?
The power rule states d/dx[ax^n] = n*a*x^(n-1); apply it term by term to differentiate a polynomial. It applies the formula d/dx[ax^n] = n*a*x^(n-1) and shows the working so you can check each step by hand.
Is the Derivative Power Rule Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.