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Unformatted text preview: x pounds of cattle t weeks after the cattle market opens for the season. The total weight of his herd is a function x = x ( t ) of the time. Express the rate of change of his prot with respect to time in terms of the derivatives of P ( x , t ) and x ( t ) . Answer: d dt [ P ( x ( t ) , t )] = b P x ( x ( t ) , t ) dollars pound Bb x ( t ) pounds week B + b P t ( x ( t ) , t ) dollars week Bb d dt ( t ) weeks week B = P x ( x ( t ) , t ) x ( t ) + P t ( x ( t ) , t ) dollars per week Lecture notes to accompany Section 14.6 of Calculus by HughesHallett et al. (1) Data adapted from Cessna 172N Information Manual , Wichita Kansas: Cessna Aircraft Company, 1978, p.516. 1...
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 Spring '07
 Hohnhold
 Calculus, Chain Rule, The Chain Rule

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