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27 November, 12:48

Find dy/dx if f (x) = (x + 1) ^2x.

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  1. 27 November, 12:56
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    u = 2x + 3

    du = 2

    v = 3x + 2

    dv = 3

    y = u/v

    y' = (v * du - u * dv) / v^2

    y' = ((3x + 2) * 2 - (2x + 3) * 3) / (3x + 2) ^2

    y' = (6x + 4 - 6x - 9) / (3x + 2) ^2

    y' = - 5 / (3x + 2) ^2

    (2x + 3) / (3x + 2) = >

    (1/3) * (6x + 9) / (3x + 2) = >

    (1/3) * (6x + 4 + 5) / (3x + 2) = >

    (1/3) * (6x + 4) / (3x + 2) + (1/3) * 5 / (3x + 2) = >

    (1/3) * 2 * (3x + 2) / (3x + 2) + 5 / (3 * (3x + 2)) = >

    2/3 + 5 / (9x + 6)

    u = 9x + 6

    u' = 9

    2 / 3 + 5 * u^ (-1)

    Derive

    0 + 5 * (-1) * u^ (-2) * u'

    -5 * 9 / (9x + 6) ^2 = >

    -5 * 9 / (9 * (3x + 2) ^2) = >

    -5 / (3x + 2) ^2

    Im in middle school to btw
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