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AP Calculus Chapter 4: Differentiation and Related Rates Practice

This chapter focuses on the differentiation of trigonometric functions, specifically sec(x)tan(x) - csc(x)cot(x). It includes implicit differentiation methods, calculating slopes of tangents at specific points, and using limits for piecewise functions to ensure differentiability and continuity. Key topics include the application of the chain rule, product rule, and quotient rule, along with basic and inverse trigonometric derivatives. Prepare for the NO CALCULATOR section with practice problems and related rates. Access online resources for additional support.

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AP Calculus Chapter 4: Differentiation and Related Rates Practice

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  1. Chapter 4 Practice AP Calculus

  2. Differentiate:

  3. sec x tan x -csc x cot x Differentiate:

  4. To the nearest thousandth, calculate the slope of the tangent where x = 4:

  5. Differentiate implicitly: Find coordinates of y when x = 4 and substitute into dy/dx equation: To the nearest thousandth, calculate the slope of the tangent where x = 4:

  6. Be prepared for NO CALCULATOR section! • Basic chain rule, product rule, quotient rule • Basic trig derivatives • Inverse trig derivatives • Implicit differentiation • Use limits to find values to make a piecewise function differentiable (and continuous). • Related Rates Ch. 4 Test Review Topics

  7. Derivatives Practice

  8. = 35 sec 5x tan 5x = = Derivatives Practice

  9. Differentiate implicitly:

  10. Derivative: Differentiate implicitly:

  11. Cylinder Volume: V = Useful Related Rates Formulas

  12. Ch. 4 R Problems, pg. 180: R4 ad, R5a, R6, R8b, R9 (pretty hard) Additional Review • Online videos, PPTS • Examples from notes • 4.2 #1-15 odd, 4.3 1-19 odd • 4.4 1-25 odd, 4.5 13-23 odd Suggested Review

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