May 19th, 2010, 02:18 AM  #1 
Senior Member Joined: Mar 2010 From: Melbourne Posts: 178 Thanks: 0  Partial derivatives
Hi, I have a question:  Let f(x,y) = x^2/x+y Obtain the first two partial derivatives f_x and f_y and evaluate them at point (2,2).  Could someone please confirm my answer?  f_x; make y constant. = 2x(x + y)^1 + x^2(x + y)^2 f_x = 2x / (x + y) + x^2 / (x + y)^2 If we sub (2,2) we have: 2(2) / (2 + 2) + 2^2 / (2 + 2)^2 = 1 + 0 = 1 ANS  f_y; make x constant. = 0(x + y)^1 + x^2(x + y)^2 f_y = x^2 / (x + y)^2 If we sub (2,2) we have: 2(2) / (2 + 2)^2 = 0 ANS  .. ? wulfgarpro. 
May 19th, 2010, 02:30 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond  Re: Partial derivatives
With y constant d/dx x^2(x + y)^1 = 2x(x + y)^1  x^2(x + y)^2 With x constant d/dx x^2(x + y)^1 = x^2(x + y)^2 
May 20th, 2010, 02:54 AM  #3 
Senior Member Joined: Mar 2010 From: Melbourne Posts: 178 Thanks: 0  Re: Partial derivatives
Evaluated at point (2,2), I get: f_x = 12/16 = 3/4 f_y = 4/16 = 1/4 ? wulfgarpro. 
May 20th, 2010, 02:58 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond  Re: Partial derivatives
Correct.


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