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A run of the mill Implicit Differentiation

  1. Apr 30, 2009 #1
    1. The problem statement, all variables and given/known data

    Use Implicit Differentiation to find y' of the equation 5x^2+ 3xy+y^2=15


    2. The attempt at a solution

    y'= (-10x-5y)/3x

    I would like to know if I did this right. Im not very confident in my math sometimes that why I came here. If i did this wrong will you please steer me right. Also if anyone could tell me how to put an equation in more like how you would write it I would appreciate that very much. (As in not the linear fashion I have done)
     
  2. jcsd
  3. Apr 30, 2009 #2
    I don't think this is correct. But, I have not done this in awhile. I think your problem is in the 2nd term [itex]3xy[/itex]. You have a product rule here.

    You have [itex]\frac{d}{dx}[3xy]=3*\frac{d}{dx}[xy][/itex]. Now what is [itex] \frac{d}{dx}[xy][/itex] ? I.e, what is the product rule?
     
  4. Apr 30, 2009 #3
    when i did the product rule i got 3y+3xy'
     
  5. Apr 30, 2009 #4

    zcd

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    Group the terms with y' and separate the terms without y' into the other side of the equation. Then you can factor out y' from one side.
     
  6. Apr 30, 2009 #5
    I did that last time then the 3y and the and the 2y (previously y^2) combine to 5y then negative after I subtract it over. what answer did you get? Also I believe I may have posted this in the wrong thread, its just a problem on a study guide.

    So after doing what you said I again got the same answer.
     
  7. Apr 30, 2009 #6

    zcd

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    You can't combine 3y and 2y because 2y is in the form (2y*y') by chain rule. 3y is a term without y', so the equation is actually 10x + 3y = -3x*y' -2y*y' (and then factor from there).
     
  8. Apr 30, 2009 #7
    oh damn it your right lol thanks thats where i thought i may have gone wrong
     
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