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Calculators / Math / Power-rule derivative
Power-rule derivative calculator
Differentiate a monomial axⁿ and evaluate it at a selected x.
On this page
Function value48
Derivative coefficient12
Derivative at x96
Calculator controls
How to calculate
Differentiate a monomial axⁿ and evaluate it at a selected x.
d/dx(a·xⁿ) = a·n·xⁿ⁻¹
Worked example
Coefficient a: 3; Exponent n: 4; Evaluation point x: 2.
Function value: 48 ; Derivative coefficient: 12 ; Derivative at x: 96 .
Assumptions and limits
This applies to one power term. Some exponent and x combinations are undefined or complex, which this real-number calculator does not represent.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Differentiate a monomial axⁿ and evaluate it at a selected x. Every assumption remains visible so the result can be checked or changed.
When this tool is useful
Use the power-rule derivative for an initial estimate, comparison, or classroom calculation.
Understanding your inputs
| Input | What to enter |
|---|---|
| Coefficient a | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Exponent n | Enter a number of at least -1000 and no more than 1000. |
| Evaluation point x | Enter a number of at least -1000000 and no more than 1000000. |
Frequently asked questions
What are the limits of this power-rule derivative?
This applies to one power term. Some exponent and x combinations are undefined or complex, which this real-number calculator does not represent.
Can I use different units?
Use the units printed beside each field. Convert measurements first when your source uses different units.