Product Plus Chain Rule: Worked Example and Solution
A complete product plus chain example with method choice, derivation, verification, and a common wrong approach.
1 problem8 min estimated timeFoundational to advanced progression
Problem
- Differentiate .
Complete worked solutions
Every problem has a source-matched answer and independently reviewed derivation.
01
Problem 1: Differentiate .
Answer:
Why this method: product plus chain matches the mathematical structure before any algebraic cleanup.
- Apply the product plus chain structure before simplifying.
- Retain every factor contributed by an inner derivative.
- A factored final form is .
- Therefore the result is .
What is included
See a concise answer and full derivation for differentiate y equals x squared e to the power (3 x).
Skills assessed
- product plus chain
Prerequisites
- basic derivative rules
- function composition
Common errors
- Applying the chain rule to a product or quotient as if it were one composition.