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 November 30th, 2016, 02:34 AM #1 Member   Joined: Sep 2013 Posts: 83 Thanks: 0 So I took this off a course book I'm reading on microeconomics note: $\displaystyle {x_1} = \phi (\bar z + {y^h} - x_2^h)$ I tried using the chain rule: $\displaystyle {{dU} \over {dz}} = {{dU} \over {d{x_1}}}{{d{x_1}} \over {dz}} + {{dU} \over {d{x_2}}}{{d{x_2}} \over {dz}}$ where I got the same expression EXCEPT for the first term, so I don't understand where the (-)sign come from: $\displaystyle - U_1^h({x_1},x_2^h)$ Last edited by skipjack; November 30th, 2016 at 06:15 AM. November 30th, 2016, 08:35 AM #2 Member   Joined: Sep 2013 Posts: 83 Thanks: 0 update: So instead of applying the normal chain rule, since: \displaystyle \eqalign{ & z = U({x_1},x_2^h) \cr & {x_1} = g({x_2}) \cr & {{dz} \over {d{x_2}}} = {{\partial f} \over {\partial {x_1}}}{{d{x_1}} \over {d{x_2}}} + {{\partial f} \over {\partial {x_2}}}{{d{x_2}} \over {d{x_2}}} = {{\partial f} \over {\partial {x_1}}}{{d{x_1}} \over {d{x_2}}} + {{\partial f} \over {\partial {x_2}}} \cr} , since $\displaystyle {x_1}$ is function of $\displaystyle x_2^h$. This seems to yield the correct expression, or maybe I've missed something ? Last edited by Ku5htr1m; November 30th, 2016 at 08:41 AM. November 30th, 2016, 03:55 PM #3 Member   Joined: Sep 2013 Posts: 83 Thanks: 0 This is from F.A.Cowell - Microeconomics - Principles and Analysis p.452-453 Tags chain, rule Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post ungeheuer Calculus 1 July 30th, 2013 05:10 PM unwisetome3 Calculus 4 October 19th, 2012 01:21 PM Peter1107 Calculus 1 September 8th, 2011 10:25 AM tarakae Calculus 1 March 13th, 2009 11:06 AM Falxix Calculus 3 May 3rd, 2008 11:33 AM

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