Which functions does this calculator support?

It supports polynomials: terms of the form ax^n where a is any real number and n is any integer or decimal exponent, plus plain constants. It does not handle trigonometric, exponential, or logarithmic functions.

How do I enter a polynomial?

Use standard notation: 3x^4 + 2x^2 - 5x + 7. Use ^ for exponents. Coefficients must immediately precede x with no spaces between them (e.g. 3x, not 3 x). Spaces around + and - signs are fine.

What is the power rule?

The power rule states that the derivative of ax^n is n·ax^(n−1). For example, the derivative of 5x^3 is 15x^2.

Why do constants disappear in the derivative?

A constant has a rate of change of zero — it does not grow or shrink as x changes — so its derivative is 0, which is dropped from the expression.

Can I compute second or higher-order derivatives?

Yes — copy the derivative result, paste it into the input, and differentiate again to get the second derivative, and so on.

Derivative Calculator

Name: Derivative Calculator
Availability: InStock
Author: Nham Vu

Enter a polynomial expression and instantly get its derivative with step-by-step power rule working shown.

Enter Polynomial

Use ^ for exponents, e.g. 3x^4 + 2x^2 - 5x + 7

f(x) =

Quick Examples

Derivative f′(x)

Enter a polynomial above to see its derivative.

Step-by-Step Working

Steps will appear here after you differentiate.

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Summary

Enter a polynomial expression and instantly get its derivative with step-by-step power rule working shown.

How it works

Type your polynomial expression in the input field (e.g. 3x^4 + 2x^2 - 5x + 7).
The calculator parses each term and identifies its coefficient and exponent.
The power rule d/dx[ax^n] = n·ax^(n−1) is applied to every term.
Constant terms differentiate to zero and are dropped from the result.
The simplified derivative and each individual step are displayed instantly.

Use cases

Check calculus homework answers for polynomial differentiation.
Quickly find the slope function of a polynomial curve.
Review power rule mechanics when studying for exams.
Verify derivatives before plugging values into physics or engineering formulas.
Teach or demonstrate differentiation step-by-step to students.
Find critical points by obtaining the first derivative of an objective function.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu