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math calculus

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Use implicit differentiation to find the equation of the tangent line to the curve xy^3+2xy=9 at the point (31). The equation of this tangent line can be written in the form y=mx+b where m is

  • math calculus - ,

    x(3y^2dy) + y^3(dx) +2xdy + 2ydx = 0

    dy (3xy^2+2x) = -dx (y^3+2y)

    dy/dx = -(y^3+2y)/(3xy^2+2x)

    I assume you mean the point (3,1)
    x = 3
    y = 1
    so
    m = dy/dx = -(1+2)/(9+6) = - 3/15 = -1/5
    put in point
    1 = m * 3 + b
    1 = -3/5 + b
    b = 8/5
    y = -x/5 + 8/5
    5y = 8-x

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