College Board-Aligned Original Notes
AP Calculus AB Unit 3 Topic 2: Implicit differentiation
Use Implicit differentiation across graphical, numerical, algebraic, and verbal representations.
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions. College Board exam weighting listed for this unit: 9%-13% of exam score.
What to Know
- Check the conditions of a theorem or method before applying it.
- Show the setup before the calculation.
- Interpret the result in context, including units when the problem supplies them.
- Always connect this topic back to the larger unit: Differentiation: Composite, Implicit, and Inverse Functions.
Detailed Notes
Implicit differentiation should be studied through multiple representations. A graph may show behavior quickly, an equation may make calculation possible, and a verbal interpretation explains what the result means.
In AP Calculus AB, AP questions often award credit for setup and reasoning, not just final answers. Write the expression, theorem, condition, or model before doing the computation.
When this topic appears in free response, check whether the question asks for a value, a rate, an interval, a comparison, or a justification. Use units and context to make the final answer precise.
Key Vocabulary
Derivative
Instantaneous rate of change of a function.
Differentiability
The property of having a derivative at a point.
Chain rule
A rule for differentiating composite functions.
Optimization
The process of finding maximum or minimum values under given conditions.
Quick Practice
How would you explain Implicit differentiation in one or two AP-style sentences?
Name the concept, apply it to a specific example or source, and explain the reasoning that connects the evidence to your answer.
Related Topics in This Unit
- The chain rule for differentiating composite functions
- Differentiation of general and particular inverse functions
- Determining higher-order derivatives of functions