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Function machine composition
Composing two functions simply means connecting together their respective function machines.
Function composition examples
Examples of composing functions to form a new combined function.
A description of how we denote functions.
Introduction to the multivariable chain rule
Introduction to the multivariable chain rule. The basic concepts are illustrated through a simple example.
Multivariable chain rule examples
Examples demonstrating the chain rule for multivariable functions.
Surfaces as graphs of functions
Illustration of how the graph of a scalar-valued function of two variables is a surface.
Special cases of the multivariable chain rule
Illustrations of different special cases of the multivariable chain rule and their relationship to the general case.
Domain of functions
How to determine the domain of a function.
A refresher on the chain rule
How to compute the derivative of a composition of functions.
The function machine
The function machine metaphor helps explain the definition and properties of a function.
Basic examples of functions illustrating the definition of a function.
Function machine parameters
Illustrating function parameters as dials that influence the behavior of a function machine.
The function machine inverse
The inverse of a function is represented by running its function machine backwards.
Inverse function examples
Examples of forming an inverse function that does undoes the action of another function.
The exponential function
Overview of the exponential function and a few of its properties.
The linear function
Overview of the linear function of one variable and a few of its properties.
The idea of the chain rule
An illustration of the basic concept of the chain rule using interactive graphics to diagram the relevant points on the graphs and the corresponding slopes.
Simple examples of using the chain rule
Basic examples that show how to use the chain rule to calculate the derivative of the composition of functions.