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Implicit Differentiation with Sin

  1. Mar 8, 2009 #1
    1. The problem statement, all variables and given/known data
    1181.jpg


    2. Relevant equations



    3. The attempt at a solution
    1181answers.jpg
     
  2. jcsd
  3. Mar 8, 2009 #2

    jgens

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    It looks like you're not applying the product rule properly when differentiating xy^2. d(xy^2) = y^2 + 2xyy'
     
  4. Mar 8, 2009 #3
    I wasn't using the product rule at all. Thank you for that! Haha.

    I tried it again and got:
    1181answer2.jpg

    Line by line:
    7= cos(xy^2)(y^2+2xyy')
    7/ cos(xy^2) = (y^2+2xyy')
    7/ cos(xy^2) - y^2 = 2xyy'
    (7/ cos(xy^2) - y^2)(2xy) = y'
     
  5. Mar 8, 2009 #4

    gabbagabbahey

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    On your last step, why are you multiplying by 2xy?....Shouldn't you be dividing instead?:wink:
     
  6. Mar 8, 2009 #5
    Yeah, it should be divided by our multiplied by (1/2xy). I'm not sure why I did that. :P

    The rest of it looks okay though?
     
  7. Mar 8, 2009 #6

    gabbagabbahey

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    the rest looks fine :smile:
     
  8. Mar 8, 2009 #7
    WOOO! It was right! Thank you very much, jgens and gabba.
     
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