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13 February, 19:41

Find y' by implicit differentiation: xy + 2x + 3x^2 = 4

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  1. 13 February, 22:04
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    (xy) ' + (2x) ' + (3x^2) ' = (4) '

    y + xy' + 2 + 6x = 0

    xy' = - y - 2 - 6x

    y' = [-y - 2 - 6x] / x

    Now solve y from the original equation and substitue

    xy + 2x + 3x^2 = 4 = > y = [-2x - 3x^2 + 4] / x

    y' = [ (-2x - 3x^2 + 4) / x - 2 - 6x ] / x

    y' = [-2x - 3x^2 + 4 - 2x - 6x^2 ] x^2 = [ - 4x - 9x^2 + 4] / x^2 =

    = [-9x^2 - 4x + 4] / x^2
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