Code Scholars Tutoring · AP Calculus AB
5–10% of the multiple-choice section. Study the concepts, conditions, and reasoning for all 6 topic codes in this unit.
Topics 3.1, 3.5
Identify outer and inner functions before differentiating. Differentiate the outer function at the inner expression, then multiply by the inner derivative. Several layers require several factors. Combine the chain rule with product or quotient rules when the top-level structure requires them. Exponential bases other than contribute a logarithmic factor. For a logarithm with base , , differentiate as on .
Read lesson and worked example →Topics 3.2, 3.6
When a relation defines implicitly as a function of , differentiating a term involving introduces . Solve algebraically for the first derivative. To obtain a second derivative, differentiate the first-derivative relation with product, quotient, and chain rules, then substitute known coordinates and slope. A point must satisfy the original relation.
Read lesson and worked example →Topics 3.3, 3.4
An inverse derivative uses the slope of the original function at the corresponding input, not at the same numeric argument. Require local invertibility and a nonzero original derivative. The derivatives of inverse trigonometric functions can be derived implicitly; apply the chain rule to their arguments. The principal branches determine the relevant domains.
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