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AP Calculus AB Chapter 2, Section 3

Understand the product and quotient rules, higher-order derivatives, and acceleration due to gravity. Practice problems included for comprehensive learning.

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AP Calculus AB Chapter 2, Section 3

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  1. AP Calculus ABChapter 2, Section 3 Product and Quotient Rules and Higher-Order Derivatives 2013 - 2014

  2. The Product Rule

  3. Using Product Rule • Find the derivative of

  4. Using Product Rule • Find the derivative of

  5. The Quotient Rule This might be easier to remember:

  6. Using the Quotient Rule

  7. Using the Quotient Rule

  8. Rewrite before Differentiating • Find an equation of the tangent line to the graph of at (-1, 1)

  9. Rewrite before Differentiating

  10. Derivatives of Trigonometric Functions

  11. Differentiating Trigonometric Functions

  12. Different Forms of a Derivative • Differentiate both forms of

  13. Higher-Order Derivatives • Higher-Order derivatives involve finding second derivatives, third derivatives, fourth derivate, and so on. • We differentiated the position function to find the instantaneous velocity, and if we find the derivative of that velocity function we will find instantaneous acceleration. • In other words, to find the acceleration at any given point, we would take the second derivative of the position function. • To find the second derivative, you just take the derivative of the first derivative. You can keep using this method to find subsequent derivatives if needed. (In this course we will stick to first and second derivatives) • Second derivatives are noted by , , , .

  14. Finding Acceleration Due to Gravity • Because the moon has no atmosphere, a falling object on the moon encounters no air resistance. In 1971, astronaut David Scott demonstrated that a feather and a hammer fall at the same rate on the moon. The position function for each of these falling objects is given by where s(t) is the height in meters and t is the time in seconds. What is the ratio of Earth’s gravitational force to the moon’s?

  15. Acceleration problem cont’d. • To find the acceleration, differentiate the position function twice. • (the Earth’s gravity pull is -9.8 meters per second)

  16. Ch. 2.3 Homework • Pg. 126 – 129: 3, 11, 13, 17, 21, 25, 29, 35, 37, 39, 43, 45, 51, 59, 61, 73, 79, 93, 97, 117 • Total Problems: 20

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