AP Calculus AB Unit 2: Differentiation - Definition and Fundamental Properties

Collector: Ann V.

The eleven lessons in Unit 2 of the flipped math calculus course take up the definition and fundamental differentiation properties. Lessons include teaching scholars how to use their knowledge of the formula to find the average rate of change to find the instantaneous rate of change and find the derivative of a function by applying the definition using limits. Pupils also learn to estimate the derivative of a function at a point by using the derivative functionality of their graphing calculators and how differentiability and continuity relate to each other. In other lessons, participants learn the power rule that allows for a shortcut to take the derivative of terms to power, more rules to use as shortcuts to find derivatives, and how to use the rules to find the equations of the tangent line and the normal line at a given point. Derivatives of the two basic trigonometric functions, cosine, and sine, the product rule of finding the derivative of two functions' product. Using the quotient rule to determine the derivative of two quotients is the focus of subsequent lessons. Finally, pupils see the derivatives of the other four trigonometric functions and begin to memorize the rules. The unit-ending review asks pupils to work through 20 problems to demonstrate what they have learned about differentiation.

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