Mathematics · Calculus
Power Rule Derivative Calculator
Differentiate a monomial axⁿ and evaluate its derivative at a selected x-value.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Start with f(x) = 3x^4.
- Multiply coefficient by power: 3 × 4 = 12; reduce power to 3.
- f′(2) = 12 × 2^3 = 96.
Definition and formula
The power rule multiplies by the exponent and reduces the exponent by one. The derivative gives the instantaneous rate of change.
If f(x) = axⁿ, then f′(x) = an xⁿ⁻¹
Worked example
For f(x) = 3x⁴, f′(x) = 12x³; at x = 2 the derivative is 96.
Common mistake
Reduce the exponent after multiplying the coefficient by the original exponent.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Power-rule derivative do?
Differentiate a monomial axⁿ and evaluate its derivative at a selected x-value.
How does the Power-rule derivative work?
The calculator applies If f(x) = axⁿ, then f′(x) = an xⁿ⁻¹. The power rule multiplies by the exponent and reduces the exponent by one. The derivative gives the instantaneous rate of change.
What can I learn from the Power-rule derivative?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.