1. Section 2.5 Chain Rule Math 1231: Single-Variable Calculus

2. 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) = x 2 +1, then f o g (x) = f(g) = sqrt(g) = sqrt(x 2 +1); g o f (x) = g(f) = f 2 +1 = x + 1. Example: f(x) = sin(x), g(x) = e x, then f o g (x) = f(g) = sin(g) = sin(e x ); g o f (x) = g(f) = e f = e sin(x) ; Example: Given y = sqrt(x 2 +1), find f(x) and g(x) such that f o g = sqrt(x 2 +1).

3. Chain Rule

4. Examples

6. Summary

7. More Examples