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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":
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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
the slope of the tangent at a point 
.
at 
is defined as: 
as long as the limit exists.
, if its derivative exists at 
