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C4 implict equation question help please! watch

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    y/x - 2x/y =1 where x>0 y>0

    show that dy/dx = y/x
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    (Original post by Tenchu)
    y/x - 2x/y =1 where x>0 y>0

    show that dy/dx = y/x
    Right this looks fairly tricky...

    y/x - 2x/y = 1

    So: [x(dy/dx) - y]/x2 - [y(2) - 2x(dy/dx)]/y2 = 0

    [ use of the quotient rule twice ]

    x(dy/dx)/x2 - y/x2 - 2y/y2 + 2x(dy/dx)/y2

    => (dy/dx)[x-1 + 2x/y2] = y/x2 + 2y/y2

    => (dy/dx) = [y/x2 + 2y-1]/[x-1 + 2x/y2]

    => dy/dx = [y(x-2 + 2y-2)] / [x(x-2 + 2y-2)]

    => dy/dx = y/x

    I bet someone has beaten me to this one.
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    thanks man, it's all so clear now.
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    (Original post by Tenchu)
    thanks man, it's all so clear now.
    lol. Not to me it isn't.

    The implicit stuff is tough.
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    That was a horrible question! Where did you find it?
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    ye it is a tough question, worth 7 marks, it's from a C4 mock paper published by Delphis (the questions are harder than usual)
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    (Original post by Tenchu)
    ye it is a tough question, worth 7 marks, it's from a C4 mock paper published by Delphis (the questions are harder than usual)
    Is there anyway that you could send the Delphis papers to me? Know of anywhere they are online etc?

    I only have Solomon papers and I am running out fast. :eek:
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    I don't have a scanner and I don't think they are available online, sorry mate
 
 
 
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Updated: June 19, 2005
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