patty's calculus videos

part 2 - derivatives (11 videos)                      back to playlists

Part 2 - Derivatives - Video 1
Section 1: Tangent Lines and Slopes
Lesson 1: Tangent Lines, Slope Formula (1:00:39)

We begin by developing an intuitive definition of the tangent line to a curve (0:30). Next, we develop a more precise definition of the tangent line (21:24).

Part 2 - Derivatives - Video 2
Section 1: Tangent Lines and Slopes
Lesson 2: Definition of the Derivative (55:14)

We complete the example begun in the previous lesson, finding the slope of the tangent line to the parabola f(x) = x^2 (0:40). Next, we define the derivative of a function (30:50).

Part 2 - Derivatives - Video 3
Section 1: Tangent Lines and Slopes
Lesson 3a: Average Velocity (35:24)

We discuss the idea of velocity, calculating your average velocity on a driving trip (0:33). Next, we look at your average velocity in the driving example over shorter and shorter time intervals (10:06).

Part 2 - Derivatives - Video 4
Section 1: Tangent Lines and Slopes
Lesson 3b: Instantaneous Velocity (46:33)

We drop a pumpkin from the top of the Chase Building (0:40) and find its average velocity (6:37) and its instantaneous velocity (9:55).

Part 2 - Derivatives - Video 5
Section 2: Rates of Change, Differentiability
Lesson 1: Average and Instantaneous Rates of Change (50:46)

We review the average and instantaneous velocity, then extend the definitions of these to the average and instantaneous rate of change of any output with respect to any input (0:40).

Part 2 - Derivatives - Video 6
Section 2: Rates of Change, Differentiability
Lesson 2: Other Notations for f'(x), Differentiablility (46:14)

We begin by learning new notations for the derivative (0:35). We then discuss the definition of differentiability and an example of a point at which a function fails to be differentiable (16:41).

Part 2 - Derivatives - Video 7
Section 2: Rates of Change, Differentiability
Lesson 3: A Logic Lesson, Graphing f' from the Graph of f (52:33)

We begin with what we learned about differentiability in the previous lesson (0:56). Then we use a logic lesson to develop a theorem that relates differentiability and continuity (2:30).

Part 2 - Derivatives - Video 8
Section 3: The Chain Rule
Lesson 1a: Chain Rule, General Power Rule (57:19)

We introduce a rule for differentiating a composition of functions, f(g(x)), called the Chain Rule (0:36). We learn a quick and easy way to apply the Chain Rule (13:50).

Part 2 - Derivatives - Video 9
Section 3: The Chain Rule
Lesson 1b: Chain Rule, General Power Rule (37:20)

We discuss a special case of the Chain Rule, called the General Power Rule (0:46). We decide whether or not we can use the General Power Rule in each of two examples (8:23).

Part 2 - Derivatives - Video 10
Section 3: The Chain Rule
Lesson 2: More Challenging Examples (54:46)

You are asked to try a tough example that involves the Chain Rule and another rule of differentiation (0:38). Together we work a tough example that involves the Chain Rule and a quotient (9:51).
 

Part 2 - Derivatives - Video 11
Section 3: The Chain Rule
Lesson 3: The Derivative of a^x, Chain Rule Alternate Notation (47:04)

First, we by learn how to use the Chain Rule to find a formula for the derivative of a^x (and see why it holds) (0:56). We then apply our new formula to several examples (18:03).