Calculus
Treating the Derivative of a Product as a Product of Derivatives
Students find the derivative of a product by differentiating each factor and multiplying the results.
Quick check
Why students make it
The rule feels like it should match constant multiples, where the derivative can pass through multiplication by a constant. The mistake is treating two changing factors as if they do not affect each other.
The rule done right
Use the product rule: if , then . Keep one factor unchanged while differentiating the other, then add the two terms.
Related resources
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Product Rule vs Quotient Rule Infographic -
Derivative Rules Visual Guide Infographic -
Derivatives Infographic -
The Chain Rule Infographic - Derivatives & Differentiation Rules Cheat Sheet
- Common Derivatives & Integrals Table Cheat Sheet
- AP Calculus AB Formula Sheet Cheat Sheet
- Tangent Lines & The Derivative as a Limit Cheat Sheet
- Calculus, Derivatives Worksheet
- Calculus, Derivative Rules, Power, Chain, Product, Quotient Worksheet
- Derivatives and Differentiation Rules Worksheet
- Calculus, Applications of Derivatives, Optimization Worksheet
- Derivative Rules Step-by-Step Tool
- Derivative & Integral Visualizer Tool
- Function Graph Explorer Tool
- Curve Sketching Explorer Tool
- Derivatives & Tangent Lines Lab Lab
- Optimization & Related Rates Lab Lab
- Limits & Continuity Lab Lab