Problem set 0 solution

# Problem set 0 - Microeconomics ECON 100A Problem Set 0 Solutions Due(Solutions Posted October 1 2010 Professor Michael Noel University of

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ECON 100A Problem Set 0 Solutions Due September 29, 2010 (Solutions Posted October 1, 2010) Professor Michael Noel University of California San Diego 1. Find the first and second derivatives for the following functions of x. a. f(x) = a + bx + cx 2 + dx 3 dx c x f dx cx b x f 6 2 ) ( 3 2 ) ( 2 + = + + = b. f(x) = ln(4x 3 ) 2 3 2 3 ) ( 3 4 12 ) ( x x f x x x x f - = = = 2. Let z = 4x 4 y 3 - 5x 2 y + xy 2 a. Derive the first and second partial derivatives for z. What is true about the cross partials? y x y x x y y x z y x z x y x y y x z y x z y x y x y x y x z y x z y y x x y x z y x z xy x y x y y x z y x z y xy y x x y x z y x z yx yy xy xx y x 2 10 48 ) , ( ) , ( 2 24 ) , ( ) , ( 2 10 48 ) , ( ) , ( 10 48 ) , ( ) , ( 2 5 12 ) , ( ) , ( 10 16 ) , ( ) , ( 2 3 2 4 2 2 2 3 2 3 2 2 2 2 2 4 2 3 3 + - = = + = = + - = = - = = + - = = + - = = Note that ) , ( ) , ( y x z y x z yx xy = b. Derive the total differential of z. dy

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## This note was uploaded on 05/07/2011 for the course ECON 100A taught by Professor Staff during the Fall '08 term at UCSD.

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Problem set 0 - Microeconomics ECON 100A Problem Set 0 Solutions Due(Solutions Posted October 1 2010 Professor Michael Noel University of

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