Second Derivatives via Implicit Differentiation
The challenge
Step-by-step procedure
Worked example 1: circle
Worked example 2
Worked example 3: evaluating at a point
Alternative method: implicit differentiation twice
Comparison of methods
AP exam tips
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Vocabulary
Unit 3 topics
Unit 3 overview13.1 The Chain Rule23.2 Applying the Chain Rule33.3 Implicit Differentiation43.4 Differentiating Inverse Functions53.5 Differentiating Inverse Trigonometric Functions63.6 Selecting Procedures for Calculating Derivatives73.7 Applying Multiple Differentiation Rules83.8 Calculating Higher-Order Derivatives93.9 Second Derivatives of Implicit Equations103.10 Connecting Derivatives and Limits