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AP Calculus AB/BC · Advanced Placement (AP) · Unit 3 of 10 · Gatekeeper unit

3Unit 3: Differentiation: Composite, Implicit & Inverse Functions

Work through these 6 topics in order. Clear the gatekeeper and the rest of the course opens up.

Contents

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  1. 3.1
    3.1 The chain rule

    A composite function is one function inside another.

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  2. 3.2
    3.2 Implicit differentiation

    When an equation is not solved for yy, treat yy as a hidden function of xx.

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  3. 3.3
    3.3 Differentiating inverse functions

    An inverse function is the graph reflected across y=xy=x, so its tangent slopes are RECIPROCALS of the original’s at the matching (reflected) point.

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  4. 3.4
    3.4 Derivatives of inverse trigonometric functions

    The inverse-trig derivatives are clean algebraic expressions (no trig left) — memorize them, and apply the chain rule to any inner function.

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  5. 3.5
    3.5 Selecting procedures for derivatives

    Before differentiating, read the STRUCTURE: is it a product, a quotient, a composite, or an implicit equation?

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  6. 3.6
    3.6 Higher-order derivatives

    Differentiate again to get the rate of the rate.

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