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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 cross-partial derivative. If you understand what to do but get tripped up on the algebra on thethe cross-partial derivative....
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- Spring '08