Derivative Calculator — Differentiate Step by Step (Free)

Use this free derivative calculator to differentiate a function. Enter a polynomial like 3x^3 - 2x^2 + 5x - 7 and it applies the power rule term by term, shows every step, and can evaluate the derivative at a point — or switch to numeric mode to differentiate any function at a chosen x.

How to use the derivative calculator

1. Enter a polynomial in x (or switch to numeric mode for any function).
2. Optionally enter a point to evaluate the derivative there.
3. Press Calculate to see the derivative and the steps.

The power rule

The derivative of a power is d/dx(a·xⁿ) = a·n·xⁿ⁻¹. Differentiating a polynomial just means applying this rule to each term and adding the results, which is exactly what the calculator does.

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Frequently asked questions

What is the power rule for derivatives?

d/dx(a·xⁿ) = a·n·xⁿ⁻¹. For example, the derivative of 3x³ is 9x².

Can it differentiate any function?

Polynomials are handled exactly with full steps. For other functions, the numeric mode gives the derivative at a chosen point using a symmetric difference.

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Can I evaluate the derivative at a point?

Yes — enter an x value and the tool reports f′(x) there in addition to the derivative expression.

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Read the full lesson: learn the method step by step.

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