Basic Chain Rule: Worked Example and Solution
A complete basic chain rule 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: Basic chain rule matches the mathematical structure before any algebraic cleanup.
- Use the power rule on the outer power .
- Multiply by the inner derivative .
- Therefore the result is .
What is included
See a concise answer and full derivation for differentiate y equals (3 x plus 2) to the power (5).
Skills assessed
- Basic chain rule
Prerequisites
- basic derivative rules
- function composition
Common errors
- Lowering the power but forgetting the derivative of the inner linear function.