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Derivative Calculator

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Derivative Calculator (power rule)

How to use: Find the derivative of a single power term ax^n (rate of change). Enter Coefficient (number in front of variable) and Power (exponent of x). Results show derivative using power rule. Formula: d/dx(ax^n) = n·a·x^(n-1). Example: For 3x⁴, enter coefficient=3, power=4 → derivative = 12x³. For 5x², enter 5 and 2 → derivative = 10x. Applications: physics velocity/acceleration (derivative of position), economics marginal cost/revenue, optimization finding maximums/minimums, engineering rate problems. Derivative represents instantaneous rate of change or slope of tangent line. Essential for calculus, physics, engineering, and mathematical modeling. Used in machine learning optimization algorithms.

Derivative Calculator — Power Rule

Find the derivative of a single term ax^n with the power rule. Basic derivative calculator for study checks. No integrals, limits or step-by-step.

This derivative calculator applies the power rule to one term of the form ax^n. You enter the coefficient a and the power n, and it returns the derivative n·a·x^(n−1).

It is deliberately simple. It does not calculate integrals or limits, it does not differentiate sums, products, quotients, trigonometric, exponential or logarithmic functions, and it does not show step-by-step working. Use it for quick checks of homework or revision answers on single polynomial terms.

The power rule

For a function f(x) = ax^n, the derivative is f'(x) = n·a·x^(n−1). Multiply the coefficient by the power, then reduce the power by one.

For a polynomial with several terms, differentiate each term separately and add the results. This calculator handles one term at a time, so enter each term in turn.

What this calculator supports

Supported: the derivative of a single term ax^n, for a numeric coefficient and power n, including fractional and negative powers. The coefficient is multiplied by the power (rounded to at most six decimal places) and the new power is n − 1.

Not supported: integrals, limits, multi-term expressions, product, quotient and chain rules, trigonometric, exponential and logarithmic derivatives, and step-by-step solutions. The result is shown in simplified form: a power of 1 gives just the coefficient and x (5x² gives 10x), and a power of 0 gives just a number (5x gives 5).

How to use this calculator

  1. Enter the coefficient, the number in front of x.
  2. Enter the power, the exponent of x.
  3. Click Calculate Derivative.
  4. Read the result as a coefficient followed by x and the new power, for example 12x^3 means 12x³. For several terms, repeat for each term and add the results yourself.

Example: the derivative of 3x⁴

Enter coefficient 3 and power 4.

Multiply 3 × 4 = 12 and reduce the power: 4 − 1 = 3.

The calculator shows 12x^3, which is 12x³.

Frequently asked questions

What can this derivative calculator do?

It finds the derivative of a single term ax^n using the power rule. For example, 5x² gives 10x.

Does it calculate integrals or limits?

No. It only calculates derivatives of single power terms. It does not do integrals, limits, differential equations or step-by-step solutions.

Can I differentiate a whole polynomial?

Not in one go. Differentiate each term separately using the calculator and add the results. For example, for 3x⁴ + 5x², calculate 3x⁴ and 5x² separately.

Does it handle constants, x on its own or sin(x)?

Constants and x on their own are covered by the power rule (a constant is ax⁰ and x is 1x¹), and the result is shown simplified (a constant gives 0, 5x gives 5). Functions such as sin(x), e^x and ln(x) are not supported.

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