Composing & Decomposing
In this section we will learn the Chain Rule for differentiating composite functions and the Generalized Power Rule for differentiating powers of functions.
Composing Functions
Composite functions are simply functions of functions: The composition of f(x) with g(x) is f(g(x)).
A.1: Find f(g(x)).
A.2: Find f(g(x)).
Decomposing Functions
Besides building compositions out of simpler functions, we can also decompose functions into compositions of simpler functions by identifying the inside function and outside function.
B.1: Find functions f(x) and g(x) such that the following expression is the composition f(g(x)).
B.2: Find functions f(x) and g(x) such that the following expression is the composition f(g(x)).
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