14209an8.4-6

# 14209an8.4-6 - (the partial derivative of f with respect to...

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c ± Kendra Kilmer April 23, 2009 Section 8.2 - Partial Derivatives First-Order Partial Derivatvies Given z = f ( x , y ) , we deﬁne the ﬁrst-order partial derivatives of f with respect to x and y : Example 1: Find the ﬁrst-order partial derivatives of the following functions: a) f ( x , y ) = x 2 - y 2 b) f ( x , y ) = 2 x 2 - 3 x 2 y + 5 y + 1 c) f ( x , y ) = 4 x 2 - y 2 x 2 + 2 y 2 d) f ( x , y ) = ln ( 3 x 2 + xy - y 8 ) 4

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c ± Kendra Kilmer April 23, 2009 Example 2: The productivity of an airplane manufacturing company is given approximately by the Cobb-Douglas production function f ( x , y ) = 40 x 0 . 3 y 0 . 7 a) Find f x ( x , y ) and f y ( x , y ) b) If the company is currently using 1500 units of labor and 4500 units of capital, ﬁnd the marginal productivity of labor (the partial derivative of f with respect to labor) and the marginal productivity of capital
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Unformatted text preview: (the partial derivative of f with respect to capital) c) For the greatest increase in productivity, should the management of the company encourage increased use of labor or increased use of capital? Second-Order Partial Derivatives Given z = f ( x , y ) there are four second order partial derivatives: 5 c ± Kendra Kilmer April 23, 2009 Example 3: Find all second-order partial derivatives of the following functions: a) f ( x , y ) = x 3 y 2 b) f ( x , y ) = xye xy Section 8.2 Homework Problems: 5,7,9,13,15,19,23,27,31,35,39,43,51,59,65,69,75,77,81,93,97 6...
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## This note was uploaded on 03/27/2012 for the course MATH 142 taught by Professor Drost during the Fall '08 term at Texas A&M.

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14209an8.4-6 - (the partial derivative of f with respect to...

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