March 8th, 2017, 10:26 AM  #1 
Newbie Joined: Mar 2017 From: Yes Posts: 2 Thanks: 0  finding dy/dt dy/dt = x^2 + xy y^2 and dx/dt = 8 when x = 6 Whenever I seem to try to do this problem, I can't get the y at the end to cancel and if I do it never is the correct answer. Last edited by skipjack; March 8th, 2017 at 11:34 AM. 
March 8th, 2017, 11:06 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,169 Thanks: 472 Math Focus: Calculus/ODEs 
Is that the entirety of the information you were given?

March 8th, 2017, 11:34 AM  #3 
Newbie Joined: Mar 2017 From: Yes Posts: 2 Thanks: 0 
yes

March 8th, 2017, 11:53 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,065 Thanks: 1621 
You are told (but omitted to tell us) that y > 0, so when x = 6, y must equal 9. Substituting y = 9 in your answer gives dy/dt = (96  72)/(6  18) = 14. The above assumes the intended question is "Find dy/dt where x² + xy  y² = 9 and dx/dt = 8 when x = 6". Last edited by skipjack; March 12th, 2017 at 06:17 AM. 
March 12th, 2017, 04:42 AM  #5  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,198 Thanks: 872  Is this really "dy/dt" or is it the original function, y, for which you want to find the derivative? Quote:
Quote:
 

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dy or dt, finding 
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