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Math Help - derivative

  1. #1
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    derivative

    If x + y = xy

    then dy/dx is?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Mr_Green View Post
    If x + y = xy

    then dy/dx is?
    You can solve the equation for y, but it is simpler to use implicit differentiation (which I presume is what they want here.)
    x + y = xy <-- Take the derivative.

    1 + \frac{dy}{dx} = y + x \cdot \frac{dy}{dx}

    \frac{dy}{dx} - x \cdot \frac{dy}{dx} = y - 1

    (1 - x)\frac{dy}{dx} = y - 1

    \frac{dy}{dx} = \frac{y - 1}{1 - x}

    Now, if you need a form of dy/dx explicitly in terms of y, then
    x + y = xy

    y - xy = -x

    y(1 - x) = -x

    y = -\frac{x}{1 - x}

    You can either just take the derivative of this (not that hard to do) or plug this expression for y into dy/dx and simplify.

    -Dan
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  3. #3
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    i was given multiple choice possibilities of

    a= 1/(x-1)

    b= (y-1)/(x-1)

    c= (1-y)/(x-1)

    d= x+y-1

    e= (2-xy)/y


    so if i multiply numerator and denominator by -1, the answer would be C, correct?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Mr_Green View Post
    i was given multiple choice possibilities of

    a= 1/(x-1)

    b= (y-1)/(x-1)

    c= (1-y)/(x-1)

    d= x+y-1

    e= (2-xy)/y


    so if i multiply numerator and denominator by -1, the answer would be C, correct?
    Yup!

    -Dan
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