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**Unformatted text preview: **the relation and get Applying the chain rule, we obtain It is usually desirable to express as a function of x alone, so we substitute 2 x 2 for u to obtain dy dx = 4 x 2 2 x 2 + 1 = 2 x 2 x 2 + 1 . ( Marginal Cost and Time Rate of Change ) The cost of manufacturing x cases of cereal is C dollars, where . Weekly production at t weeks from the present is estimated to be x = 6200 + 100 t cases. (a) Find the marginal cost, (b) Find the time rate of change of cost, (c) How fast (with respect to time) are costs rising when t = 2? (a) We differentiate C ( x ). (b) To determine , we use the Chain Rule. Now we rewrite x in terms of t using x = 6200 + 100 t . (c) With respect to time, when t = 2, costs are rising at a rate of...

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