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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

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 "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 examplesâ€”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 functionContinuity and Differentiability Definition of continuity Definition of differentiability Derivative of an absolute value Application of logarithms`

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