Week 6: Differentiation: tangents and derivative at a point, the derivative as a function, differentiation rules,

Thomas Calculus, Early Transcendentals, (13th edition)

Chapter 3 Derivatives

The derivative is one of the key ideas in calculus, and is used to study a wide range of problems in mathematics, science, economics, and medicine. These problems include finding points where a continuous function is zero, calculating the velocity and acceleration of a moving object, determining how the rate of flow of a liquid into a container changes the level of the liquid within it, describing the path followed by a light ray going from a point in air to a point in water, finding the number of items a manufacturing company should produce in order to maximize its profits, studying the spread of an infectious disease within a given population, or calculating the amount of blood the heart pumps in a minute based on how well the lungs are functioning.

Sec 3.1 Tangents and Derivative at a Point (pages: 123 - 127)

In this section we define the slope and tangent to a curve at a point, and the derivative of a function at a point. The derivative gives a way to find both the slope of a graph and the instantaneous rate of change of a function.

Sec 3.2 The Derivative as a Function (pages: 128 - 135)

In this section, we investigate the derivative as a function derived from ƒ by considering the limit at each point x in the domain of ƒ.

Sec 3.3 Differentiation Rules (pages: 136 - 146)

This section introduces several rules that allow us to differentiate constant functions, power functions, polynomials, exponential functions, rational functions, and certain combinations of them, simply and directly, without having to take limits each time.