Power Rule Calculator

Work out power rule instantly with clear inputs, formula shown and shareable results.

About Power Rule Calculator

The power rule says d/dx (a·xᵖ) = a·p·x^(p−1), reducing the exponent by one and multiplying by the old exponent. Reversing it gives the antiderivative a·x^(p+1)/(p+1), valid whenever p ≠ −1.

Formulas

Power rule

d/dx (a·xᵖ) = a·p·x^(p−1)

Reverse power rule

∫a·xᵖ dx = a·x^(p+1)/(p+1) + C, for p ≠ −1

Worked example

With the default values below, Power Rule Calculator returns f'(x) of 160.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Coefficient a: 5
Power p: 4
Evaluate at x: 2

Results

f'(x): 160.00000000
Derivative in symbols: 20x^3
f''(x): 240.00000000
Antiderivative at x (constant omitted): 32.00000000

Step by step

1Values used
2Power rule
3Reverse power rule
4f'(x)= 160.00000000
5Derivative in symbols= 20x^3
6f''(x)= 240.00000000
7Antiderivative at x (constant omitted)= 32.00000000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Differentiate 5x⁴ at x = 2.

20x³ = 20 × 8 = 160.

What happens at p = −1?

The antiderivative becomes a·ln|x| rather than a power, which is where the natural logarithm enters calculus.