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4.2 - DERIVATIVES - PRODUCTS AND QUOTIENTS I. Product Rule y f (x ) = g ( x ) h( x ) y = f ( x) = g ( x) h( x) + h( x ) g ( x) OR y = f ( x) = g ( x) h( x ) + h( x) g ( x) (since multiplication is commutative) Examples: II. Quotient Rule y = f ( x) = t ( x) b( x ) y = f ( x) = b( x) t ( x) t ( x) b( x) b( x ) 2 (don’t forget that subtraction is not commutative, so you cannot switch the order in the numerator) Examples: III. Marginal Average Cost, Revenue, and Profit Definitions: Cost Analysis: A machine shop makes drill bits with C ( x ) 1000 25 x 0.1x 2 . a. Find the average cost function for drill bits. b. Find the average cost of producing a drill bit at a production level of 10 drill bits per day and interpret. c. Estimate the average cost per bit at a production level of 11 drill bits per day and interpret.