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Calculation Machine

Derivative Power Rule Calculator

Differentiate a polynomial term by term.

Reviewed by the Calculation Machine team · How we check our maths

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.

The formula

d/dx[ax^n] = n*a*x^(n-1)

Worked example

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

Result

  • Derivative6x^2 + -6x + 5
  • Derivative at x17
  • Original degree3

How to use the Derivative Power Rule Calculator

  1. 1Enter the coefficients of your cubic polynomial.
  2. 2Each term's exponent is multiplied by its coefficient and the exponent drops by one.
  3. 3Optionally evaluate the resulting derivative at a specific x.

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