Derivative Calculator

Differentiate functions with respect to a chosen variable.

Use this calculator as a study checker

Enter the problem carefully, review the interpreted input, and compare each step with your own work. Calculus results can depend on notation, variables, bounds, domains, and assumptions.

  • Check the method before copying the answer.
  • Use the examples below to test nearby problems.
  • Read the calculus guides for worked explanations.

Solution

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Enter an expression or choose an example to calculate.

Derivative Examples

What this calculator is for

A derivative measures instantaneous rate of change. It is also the slope of the tangent line to a function at a point. Use it to check your setup, compare steps with your own work, and review the meaning of the final expression before copying it into homework.

How derivatives are found

  1. Simplify the function before differentiating when possible.
  2. Apply the power, product, quotient, and chain rules as needed.
  3. Check whether the answer represents slope, rate of change, or sensitivity in context.

Manual example

  1. Problem: \(\frac{d}{dx}(x^3+\sin x)\).
  2. Differentiate term by term: \(\frac{d}{dx}x^3=3x^2\) and \(\frac{d}{dx}\sin x=\cos x\).
  3. Final result: \(3x^2+\cos x\).

Common mistakes to avoid

  • Forgetting the chain rule for nested functions.
  • Using the product rule on a sum.
  • Dropping constants that multiply a function.

When to double-check the result

The derivative calculator is strongest for symbolic functions of one variable. For equations mixing x and y, use the implicit derivative calculator.

Learn the method behind this calculator

These guides explain the rules and common mistakes that often appear in derivative calculator problems.

Derivatives Derivative Rules Every Student Should Know Derivatives Chain Rule, Product Rule, and Quotient Rule Derivatives How to Apply the Chain Rule for Derivatives