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Logarithmic, Exponential, and Other Transcendental Functions

Proofs

 Tutorial Name Tutorial Description

Tutorials

 Tutorial Name Tutorial Description Logs, Exponentials and other Transcendentals (part 1) Natural logarithmic function (ln).  Definition of ln with proof. Introduction to derivative of ln(x) and the integral of 1/x. Logs, Exponentials and other Transcendentals (part 2) Properties of ln with their proofs.  Using properties to expand logarithmic expressions. Logs, Exponentials and other Transcendentals (part 3) Definition of the natural number e. Examples of logarithmic differentiation. Logs, Exponentials and other Transcendentals (part 4) Derivative involving absolute value (ln|x|). Definition of natural logarithmic integration with several examples. Logs, Exponentials and other Transcendentals (part 5) More logarithmic integration examples. Integrals of trigonometric functions involving natural logs. Ends with trig intergal table. Logs, Exponentials and other Transcendentals (part 6) Starts with a trig integral table.  Introduction to inverse funtions with a definition.  Verifying inverse functions.  Examinng the existence of an inverse funciton. Logs, Exponentials and other Transcendentals (part 7) Continuity and differentiability of inverse functions.  Derivative of an inverse function with proof.  Example of derivative of an inverse function. Logs, Exponentials and other Transcendentals (part 8) Examples of derivatives of inverse funcitons.  The natural exponential function definition.  Examples of solving exponential functions. Logs, Exponentials and other Transcendentals (part 9) Derivatives of natural exponential functions with proof.  Examples of derivatives of natural exponential functions.  Integrals of natural exponential functions definition.  Examples of integration of natural exponential functions. Logs, Exponentials and other Transcendentals (part 10) Several examples of integration of natural exponential functions.  Review of the basic properties of logarithms.  Definition of exponential functions with bases other than e. Logs, Exponentials and other Transcendentals (part 11) Examples of solving exponential and logarithmic equations.  Examples of differentiation and integration exponential functions with bases other than e. Logs, Exponentials and other Transcendentals (part 12) More examples of differentiation of exponential and logarithmic equations.  Applications of exponential functions such as compound interest.  Derivation of the natural exponential growth and decay function.  Examples involving exponential growth and decay functions such as biological growth and half life. Logs, Exponentials and other Transcendentals (part 13) More examples of applying exponential function to compound interest and derivatives of exponential functions with bases other than e.  Introduction to inverse trigonometric functions.