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Purple Monkey Dishwasher
Purple Monkey Dishwasher asked in Science & MathematicsMathematics · 1 decade ago

Easy implicit differentiation?

Find dy/dx of;

(1 + x^2)y^2 = 1- x^2

Thanks a lot.

2 Answers

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  • gudspeling
    Lv 7
    1 decade ago
    Favourite answer

    (1+x²)y² = 1-x²

    Differentiate this to get

    2xy² + 2(1+x²)yy' = -2x

    y' = (-2x-2xy²)/[2y(1+x²)]

    y' = -2x(1+y²)/[2y(1+x²)]

    y' = x(1+y²)/[y(1+x²)]

  • harry m
    Lv 6
    1 decade ago

    (1 + x^2)y^2 = 1- x^2

    => (1 + x^2)2y * y' + y^2*2x = -2 x

    => (1 + x^2)2y * y' = -2 x - y^2*2x

    => y' = ( -2 x - y^2*2x) /[(1 + x^2)2y]

    QED

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