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# L14 - Lecture 14(Sec 3.3 and 3.4 Chain Rule part II...

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Lecture 14: (Sec. 3.3 and 3.4) Chain Rule, part II; Marginals ex. A store sells a CD for \$16. If daily sales x are increasing by three CDs per day, what is the rate at which revenue is increasing with respect to time?

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Chain Rule: Rate of Change Version Let y be a differentiable function of u where u is a differentiable function of x . Then y is a differentiable function of x and ex. Suppose y = 4 u + 1 u and u = x 2 - 3. Find dy dx . What is the slope of the tangent line to y = f ( x ) when x = - 1?
ex. The quantity demanded per month, x , of a new PC is related to the unit price p by the demand equation x = f ( p ) = 12 p 640 , 256 - p 2 . It is also estimated that the average price of the PC will be given by p ( t ) = 2000 8 + t + 600, 0 t 9, where t is in months. Find the rate at which the quan- tity demanded per month will be changing 2 months from now.

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Marginal Functions in Economics ex. Let C ( x ) = 1000 + 25 x - 0 . 1 x 2 be the cost function for a product. 1) Find the rate at which cost is changing with respect to x for a production level of 100 units.
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L14 - Lecture 14(Sec 3.3 and 3.4 Chain Rule part II...

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