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

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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.

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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.

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Simplify: Applying the Product Rule:

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

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CONTINUED Combining like terms and simplifying:

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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.

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CONTINUED Applying the Product Rule:

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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:

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QUESTIONS

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Product Rule Links Product Rule Workshop Handout Product Rule Workshop Handout Product Rule Workshop Handout Product Rule Workshop Handout Product and Quotient Rules Handout Product and Quotient Rules Handout Product and Quotient Rules Handout Product and Quotient Rules Handout

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Complex Functions These derivatives involve embedded composite, product, and quotient rules. The functions f or g must be derived using another rule.

Complex Functions These derivatives involve embedded composite, product, and quotient rules. The functions f or g must be derived using another rule.

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