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Math Help - implict differential

  1. #1
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    implict differential

    please, someone help, how would i do x^2 + 2(x^2)y + 3xy = 0 with implicit differential..

    also, how would i find f'(-t cos(PI/t) (PI) (t^-2) (sin(PI/2))) there are more than two terms

    thanks
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  2. #2
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    Quote Originally Posted by Arez View Post
    please, someone help, how would i do x^2 + 2(x^2)y + 3xy = 0 with implicit differential..

    ...
    If you have a function f(x,y) = 0 then you can differentiate it using the formula:

    f(x,y)=0~\implies~\dfrac{dy}{dx}=y'=-\dfrac{\frac{\partial f}{\partial x}}{\frac{\partial f}{\partial y}}

    With your function you'll get:

    y'=-\dfrac{2x+4xy+3y}{2x^2+3x}

    ---------------------------------------------------------------------

    If you don't want to use this formula differentiate the given equation wrt x:

    x^2 + 2(x^2)y + 3xy = 0~\implies~2x+(4x\cdot y + 2x^2 \cdot y') + (3y+3x\cdot y')=0

    Expand the brackets and collect all terms containing y' at the LHS:

    2x^2y'+3xy'=-2x-4xy-3y

    Factor out y' and divide both sides by the bracket. You'll get the result which you've got by the formula too.
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