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

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.

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.