Unit 2 The Derivativeap Calculus

This AP Calculus AB class covers a review of Unit 2 on basic derivative rules.Skills1.E Apply appropriate mathematical rules or procedures, with and without.
This AP Calculus AB/BC study guide for Unit 2 covers key topics with in-depth notes on Defining the Derivative of a Function and Using Derivative Notation.

Convert “The limit of the square root of x plus 1, plus x, minus 3, as x goes to 17” into the mathematical notation for limits. Evaluate lim𝑥→−4(𝑥2+ 8𝑥−1) 4. Evaluate lim𝑥→1(−5𝑥3+ 𝑥2+ 2) In problems 5 – 8, state the problem in limit notation and what it seems to be approaching. AP Calculus AB Course Information; AB Calculus Homework. Unit 1: Functions, Graphs, Limits, and Continuity; Unit 2: The Derivative; Unit 3: Applications of the Derivative; Unit 4: The Definite Integral; Unit 5: Differential Equations and Mathematical Modeling; Unit 6: Applications of Definite Integrals; Unit 7: Review & AP Test.

Unit 2: Derivatives

In this unit, you will learn first the concept of a derivative by explaining it through limits. You will see that the limit definition and computation are drawn out, and often difficult, so you will learn shortcuts to compute derivatives. You will learn to compute derivatives for all different types of functions, as well as for combinations of functions. After you learn how to compute derivatives, you will look at what derivatives tell you specifically at any point in a function, as well as what they tell you about the function as a whole. You will finish this unit by looking at the computation and meaning of second derivatives, as well as real-life applications of derivatives. The main applications to be reviewed in this unit will be related rates problems, optimization problems, and problems involving displacement, velocity, and acceleration.

Completing this unit should take you approximately 54 hours.