1. The Product Rule Brought To You By Tutorial Services The Math Center

2. The Product Rule • This rule is used when there are two or more functions being multiplied. • The derivative of (f(x))*(g(x)) is the first function times the derivative of the second plus the second function times the derivative of the first. • When using the product rule, the order in which you derive doesn’t matter.

3. EXAMPLE 1 Product Rule: • Typically, f(x) is chosen as the first function, and g(x) as the second function, however, changing their order will not affect the solution.

4. Simplify: Applying the Product Rule:

5. Rewrite: Product Rule: Applying the Product Rule: EXAMPLE 2

6. CONTINUED Combining like terms and simplifying:

7. Product Rule: • We can also apply the Product Rule for more than two functions. • We can rewrite the Product Rule in this manner: PRACTICE SAMPLE • For more functions we can keep rewriting the Product Rule by following the pattern.

8. Applying the Product Rule: CONTINUED

9. Final Answer: CONTINUED (9x²+4)(x-5)(x+1)=(9x4-36x³-45x²+4x²-16x-20) (3x³+4x)(1)(x+1)=(3x4+3x³+4x²+4x) (3x³+4x)(x-5)(1)=(3x4-15x³+4x²-20x)

10. QUESTIONS

11. Product Rule Links • Product Rule Workshop Handout • Product and Quotient Rules Handout