AP Calculus BC September 9, 2015 Day 7 – The Chain Rule and Implicit Differentiation.

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Presentation transcript:

AP Calculus BC September 9, 2015 Day 7 – The Chain Rule and Implicit Differentiation

Entry Task – f or f’? In pairs, complete your “f or f’” problem. Some pairs will present their answers.

Review Assignment #6 Discuss the assignment with your table partners. What questions do you have? Did you solve the problems differently? When you are done, turn in the assignment.

Learning Targets  I can determine the derivative of functions using the Chain Rule.  I correctly solved problems involving the derivative of functions.  I explained Chain Rule and created an example of the Chain Rule.

The Derivative The derivative of f at x is given by provided that the limit exists. The derivative of f at x is the slope of the tangent line through x.

Differentiability and Continuity

Rules for Differentiation You can use the definition of a limit to derive many basic rules for differentiation: The Constant Rule The Power Rule The Constant Multiple Rule The Sum and Difference Rules The Product and Quotient Rules Derivatives of Trigonometric Functions

Rates of Change Since the rate of change of a function and the slope of its graph are the same thing, you can use the slope formulas to determine rates of change: Use the difference quotient to find the average rate of change Use the derivative to find the instantaneous rate of change

§2.4 The Chain Rule At your tables, construct (1) a written description and (2) a solved example of the Chain Rule.

Learning Targets  I can determine the derivative of functions using the Chain Rule.  I correctly solved problems involving the derivative of functions.  I explained Chain Rule and created an example of the Chain Rule.

Assignment #7 Due September 10 §2.4 pp : 23, 33, 48, 59, 77, 81,