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

3. 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.

4. 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.

5. Simplify: Applying the Product Rule:

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

7. CONTINUED Combining like terms and simplifying:

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

9. CONTINUED Applying the Product Rule:

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

11. QUESTIONS

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