This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Econ 300: Methods and Tools of Economic Analysis Summer 2009 Pablo M Federico DIFFERENTIATION AND APPLICATIONS 1 Univariate Derivatives Take the &rst and second derivatives of these univariate functions: 1. y = 3 x 2 +4 x x 2 +1 2. y = x 2 ln( x + 1) 3. y = x 3 e & 3 x 4. y = x 3 x 1.1 The Chain Rule Take the derivative of y with respect to t in each of the following cases: 1. y = x 2 & 2 xz 2 + z 2 x = t 2 z = 3 t 2. y = 3 x + z + xz z = & t + 7 x = 2 + t 3. y = e 3 x 2 + 4 x ln z + tz x = t 1 = 2 z = t + 7 1 2 Multivariate Functions I believe that taking the derivatives of multivariate functions and understanding how to &nd their minima and maxima is the key part of the material that we have covered in the last month. Therefore, I would recommend focusing on this section &rst. 2.1 Derivatives Take the &rst and second derivatives of the following functions with respect to x and y as well as the crosspartial derivative. If you understand what to do but get tripped up on the algebra on thethe crosspartial derivative....
View
Full
Document
This note was uploaded on 11/14/2010 for the course ECON Econ 326 taught by Professor Hayes during the Spring '08 term at University of Maryland Baltimore.
 Spring '08
 Hayes

Click to edit the document details