Unit 3
Differentiation Rules
9–13% AB & BCCED Unit 3
The Chain Rule
Differentiating composite functions: the most important rule in calculus.
The Chain Rule
If is a composite function where both and are differentiable, then:
Chain Rule
Leibniz notation: If and , then
→ Tip
"Find the derivative of the outside function with the inside staying the same; then multiply by the derivative of the inside function."
Common Chain Rule Patterns
| Function | Derivative |
|---|---|
⚠ Watch Out
Forgetting the Inside Derivative: The most common error: differentiating and getting instead of . Always ask: "Did I multiply by the derivative of the inside?"
Notation:
The expression means . So and requires the chain rule.
AP® Calculus AB & BC · Unit 3 Overview · Mr. Brantley