The Chain Rule Section 3.4

Example 1 – Chain Rule Find F ‘ (x) if F (x) = Using Equation Chain Rule: If we let u = x2 + 1 and y = , then

Example 2 – Differentiate

Example 3 – Chain Rule Differentiate y = (x3 – 1)100. Solution: Taking u = g(x) = x3 – 1 and n = 100, we have = (x3 – 1)100 = 100(x3 – 1)99 (x3 – 1) = 100(x3 – 1)99  3x2 = 300x2(x3 – 1)99

Example 4 – Chain Rule

Example 5 – Chain Rule

Example 6 – Chain Rule

Example 6 – Chain Rule

Example 7 – Chain Rule

Example 8 – Chain Rule

3.4 The Chain Rule Summarize Notes Read section 3.4 Homework Pg.205 #1,7,13,15,17,21,23,27,31,33,47,51,55,79