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Derivative Calculator

Find the derivative of a polynomial expression and evaluate the derivative at a selected x value.

  • polynomial derivative calculator
  • differentiation calculator
  • calculus derivative calculator

Status: initial

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Derivative as slope

Explore the derivative calculator result visually while keeping this page's detailed guidance and examples.

Derivative as slope
Slope at x12

Use this result well

  1. 1Verify the calculator inputs.
  2. 2Compare the key result relationships.
  3. 3Review the page guidance before acting.

The derivative value is instantaneous slope at one point.

Calculus guide

Derivative Calculator for quick, reliable checks

Find the derivative of a polynomial expression and evaluate the derivative at a selected x value. This focused polynomial tool differentiates term by term and evaluates the resulting expression at a selected x-value, making each power-rule transformation easy to audit.

When to use this derivative calculator

Use it for polynomial differentiation checks, tangent slope practice, and introductory calculus study. Use it to verify introductory calculus exercises and tangent slopes. It intentionally does not claim support for trigonometric, logarithmic, exponential, product, quotient, or chain-rule expressions.

How the calculation works

Power rule: d/dx of ax^n = a x n x^(n - 1). Constants differentiate to 0. For each axⁿ term, multiply the coefficient by n and reduce the exponent by one; the derivative of every constant term is zero.

Variable explanations

Understand what each input and result means before calculating.

Expression

Enter expression carefully because this value directly affects the result.

Coefficient

Enter coefficient carefully because this value directly affects the result.

Power

Enter power carefully because this value directly affects the result.

x value

Enter x value carefully because this value directly affects the result.

Reviewed by the Calculator.org.in Editorial Team

Formula behavior, validation cases, explanatory examples, and cited sources are checked before publication. This review supports educational accuracy and is not a substitute for qualified professional advice.

Last reviewed: 2026-08-03

Review process

Formula guide

See the calculation logic, variable definitions, and practical meaning.

Derivative Calculator

Power rule: d/dx of ax^n = a x n x^(n - 1). Constants differentiate to 0.

  • Expression
  • Coefficient
  • Power
  • x value

The calculator keeps the computation visible through labeled inputs, a primary result, and supporting checks so users can verify the answer before applying it.

Worked examples

Follow realistic inputs through the calculation step by step.

1

Worked example

Differentiate 3x^2 + 2x - 5

  1. 1Enter 3x^2 + 2x - 5.
  2. 2Apply the power rule to each term.
  3. 3The derivative is 6x + 2.
2

Worked example

Differentiate a cubic polynomial

  1. 1Enter 2x^3 - 4x^2 + 7.
  2. 2Differentiate each term with the power rule.
  3. 3The derivative is 6x² - 8x.
3

Worked example

Evaluate a tangent slope

  1. 1Enter x^2 - 3x + 2 and set x to 4.
  2. 2The derivative is 2x - 3.
  3. 3At x = 4, the derivative and tangent slope equal 5.

Common mistakes

Avoid these common input and interpretation errors.

Entering functions beyond polynomial syntax

Review this point before using the result in coursework, planning, purchasing, or documentation.

Dropping negative signs

Review this point before using the result in coursework, planning, purchasing, or documentation.

Forgetting that constants become zero

Review this point before using the result in coursework, planning, purchasing, or documentation.

Frequently asked questions

Quick answers to the questions users ask most often.

What expressions are supported?
This calculator supports polynomial expressions such as 3x^2 + 2x - 5.
Does it show symbolic calculus for trig or logarithms?
No. This release focuses on polynomial derivatives for clear, reliable student checks.
What does a derivative represent?
At a point, a derivative represents instantaneous rate of change and the slope of the tangent line when that derivative exists.
Why does the exponent decrease by one?
That is the polynomial power rule: differentiating xⁿ gives n·xⁿ⁻¹. The original exponent also becomes a coefficient multiplier.
Can the derivative be zero at a point?
Yes. A zero derivative indicates a horizontal tangent, though additional analysis is needed to decide whether the point is a maximum, minimum, or neither.

References

Sources used to support the calculator guidance.

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Version history

A transparent record of calculator content updates.

Updated 2026-08-03
  • 1.0.0 · 2026-08-03

    Initial calculator release with formula tests and SEO-ready content.