### Lecture 14:

##### Lecture Details :

Begin Test 3 Material

4.4 - 4.6 Review of Natural Logarithms: identities and properties

Derivative of y = ln x

Derivative of y = ln u, u = f(x) (Chain Rule)

##### Course Description :

Introduction to Differential Equations - Graphing by plotting points and analysis - Review slopes of lines and equations of lines - Intro to the derivative: slope of a curve at a point - Slopes of curves at points - The derivative: Notations, Rules Power Rule - Limits and the limit definition of the derivative - Continuity and differentiability at a point - More rules for derivatives - Derivatives as a rate of change - Describing graphs using words and derivaives - Using Derivatives for Curve Sketching - Optimization - Product and Quotient Rule for finding the derivative - Optimization: Geometric, Inventory, Business and Economics - Geometric,Inventory,Business and Economics - Exponential Functions - Derivative of f(x) = ex - Chain Rule for derivatives - Derivatives of y = e u where u = f(x) - Natural Logarithms - Derivative y = ln x - Applications of the Natural Exponential Function - ntidifferentiation - Integration - Riemann Sums and the Definite Integral - Consumer's and Producer's Surplus - Future Value of a Continuous Stream - Present value of a Continuous Stream

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