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    bnhunter's Avatar
    bnhunter Posts: 2, Reputation: 1
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    #1

    Nov 12, 2010, 05:55 PM
    how to find implicit differentiation?
    x^2+3xy+y^2
    bnhunter's Avatar
    bnhunter Posts: 2, Reputation: 1
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    #2

    Nov 12, 2010, 06:12 PM
    implicit differentiation
    x^2y^3 - 6xy^2 = 10
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #3

    Nov 12, 2010, 11:05 PM

    Yes, we do offer free help, but not 'free answers'... =/

    Do you know how to differentiate an expression with one variable?



    So, you can express the derivative of what you got as:



    You can differentiate the first part?

    For the second part, let me give you an example.



    As you can see, you differentiate the y similar to how you differentiate x, but you just add dy/dx after differentiating.

    For the middle part of your problem, use the product rule.
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    galactus Posts: 2,271, Reputation: 282
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    #4

    Nov 13, 2010, 10:21 AM

    If I may. Allow me to show a method I often use for implicit diff.

    Use

    i.e.







    Just a thought if anyone is interested.
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    Unknown008 Posts: 8,076, Reputation: 723
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    #5

    Nov 14, 2010, 03:00 AM

    I wasn't sure what you did at first, but when I expanded it, I understood. Interesting method :)

    You only missed a 'y' in the denominator ;)

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