Section 2.5 Chain Rule

Math 1231: Single-Variable Calculus

Composite Function

Given f(x) and g(x), y = f( g(x) ) is called a composite function, which is denoted by y = f o g (x) .

Example: f(x) = sqrt(x), g(x) = x2+1, then f o g (x) = f(g) = sqrt(g) = sqrt(x2+1); g o f (x) = g(f) = f2+1 = x + 1.

Example: f(x) = sin(x), g(x) = ex, then f o g (x) = f(g) = sin(g) = sin(ex); g o f (x) = g(f) = ef = esin(x);

Example: Given y = sqrt(x2+1), find f(x) and g(x) such that f o g = sqrt(x2+1).

Chain Rule

Examples

Examples

Summary

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