What is the product rule?
(uv)′ = u′v + uv′.
Product Rule Calculator
Differentiate a product uv using (uv)′ = u′v + uv′ for linear or power factors.
Enter u and v
Choose linear or power mode and provide the parameters.
About this calculator
How to use Product Rule Calculator, plus the formulas and logic behind the results.
Tool description
The product rule is a fundamental differentiation formula for products of differentiable functions.
How to use
- Select linear factors or power factors.
- Enter the corresponding coefficients or exponents.
- Select Calculate to view (uv)′ expanded.
- Optionally expand and compare with differentiating uv first.
Formulas & reference
(uv)′ = u′v + uv′Powers: (xᵐ xⁿ)′ = (m+n) xᵐ⁺ⁿ⁻¹
Product rule tips
- Do not multiply derivatives u′v′ alone
- Quotient rule is related but different
- Powers check: product of powers is a single power
- Linear×linear yields a quadratic derivative that is linear
Calculation logic
Computes u′, v′, forms u′v+uv′, and also shows the simplified combined polynomial or power.
Educational cases only—not a general symbolic differentiator.
Product Rule Calculator FAQ
Common questions about this calculator and how to use the results.
Why two modes?
Linears are common in Calc I; powers illustrate combining exponents.
Is FOIL needed first?
You can expand uv then differentiate; the product rule should match.
What about three factors?
Use (uvw)′ = u′vw + uv′w + uvw′ by extension.
Can exponents be negative?
Yes in power mode—interpret as rational powers carefully at x=0.
Is this free?
Yes.