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Unformatted text preview: Math 135 Business Calculus Spring 2009 Class Notes 1.6 Differentiation Techniques: The Product and Quotient Rules In Section 1.5, we saw how to differentiate the sum of two functions. This section shows how to differentiate the product or quotient of two functions. THE PRODUCT RULE While the derivative of the sum of two functions is the sum of the derivatives, the derivative of a product of two functions is not the product of the derivatives. The following is the rule for finding the derivative of a product. THEOREM 5 The Product Rule Let F ( x ) = f ( x ) g ( x ). Then F ( x ) = d dx f ( x ) g ( x ) = f ( x ) g ( x ) + f ( x ) g ( x ) . EXAMPLE Find d dx ( x 4 2 x 3 7)(3 x 2 5 x ) . EXAMPLE Find d dx ( x 3 3 x 2 + x ) 2 . EXAMPLE The U.S. gross domestic product, in billions of dollars, can be approximated using the function P ( t ) = 567 + t (36 t . 6 104) where t is the number of years since 1960....
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