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The Derivative and Basic Differentiation

Topic Review on "Title":

Slope of the tangent at a Point:
As the slope of the tangent at a point

Definition of a Function:
The derivative of at is defined as: as long as the limit exists.

Definition of differentiability:
A function is differentiable at a point , if its derivative exists at

Rapid Study Kit for "Title":
Flash Movie Flash Game Flash Card
Core Concept Tutorial Problem Solving Drill Review Cheat Sheet

"Title" Tutorial Summary :

The derivative is one of the most important principles in a Calculus course. This tutorial introduces the derivative, its properties and its operations that are needed in application problems such as the continuity and differentiability of functions.

The tangent line to a curve is discussed with the introduction of examples. The slope of the tangent at a point idea is discussed with graphs and the definition of the slope of the tangent. The derivative of a function is presented in many forms. The continuity and differentiability principles are presented with the concept of derivatives.

Tutorial Features:

Specific Tutorial Features:

  • Examples to illustrate the properties and applications of derivatives.
  • Animated diagrams to actually show the inverse relationship between a derivative and their applications.
  • Problem-solving techniques are used to work out and illustrate the example problems using step by step presentation.

Series Features:

  • Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
  • Definition slides introduce terms as they are needed.
  • Visual representation of concepts
  • Animated examples—worked out step by step
  • A concise summary is given at the conclusion of the tutorial.

"Title" Topic List:
Slope of a Tangent Line at a Point
Slopes of tangents
Definition of the slope of tangent
Definition of the derivative of a function
Continuity and Differentiability
Definition of continuity
Definition of differentiability
Derivative of an absolute value
Application of logarithms

See all 24 lessons in college calculus, including concept tutorials, problem drills and cheat sheets:
Teach Yourself College Calculus Visually in 24 Hours