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Derivative question! Exam tomorrow, need to understand this asap!

  1. Oct 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Hey all!

    Ok, doing a simple implicit differential.


    x^3 + y^3 = 6xy

    The 6xy is messing me up! How do I differentiate that??

    The book says 6xy turns into 6y + 6xy'

    I do not understand how to differentiate 6xy (how the x and y are stuck together)

    Ok, doing a simple implicit differential.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 30, 2012 #2

    Mentallic

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    Homework Helper

    [tex]\frac{d}{dx}(xy)=\frac{dx}{dx}\cdot y + x\cdot \frac{dy}{dx}[/tex]

    Notice how it's the product rule?
     
  4. Oct 30, 2012 #3
    Yes I know its the product rule....

    Wait. Ahh, I see!!!

    6x is f and y is g (in terms of f'g + fg')

    which gives me

    (6y) + 6x(y')

    :)

    Thanks!
     
  5. Oct 30, 2012 #4
    But now that brings me to my 2nd question.

    This leaves me with: x^2 + y^2y' = 2y + 2xy'

    I don't understand how to solve for y' when I have 2 of them.
     
  6. Oct 30, 2012 #5

    Dick

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    Use algebra! Move both y' terms to one side of the equation everything else to the other side and solve for it.
     
  7. Oct 30, 2012 #6
    ahhg, I think I need to stop. I am forgetting such silly things!!!!

    I got the question. Thanks guys. Think its time for little break :)
     
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