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posted by on .

Find the derivative of the function y defined implicitly in terms of x.
y = sqrt(xy + 9)

Please help! Thanks! :)

  • Calculus - ,

    Did you mean "with respect to x" ?
    If so then I would square both sides
    y^2 = xy + 9
    2y dy/dx = x dy/dx + y
    2y dy/dx - x dy/dx = y
    dy/dx(2y-x) = y
    dy/dx = y/(2y-x) such that √(xy-9) ≥ 0

    if you want that expression to be in terms of x only, (like you typed)
    we have a mess ahead
    we would have to solve
    y^2 - xy - 9 = 0 for y in terms of x
    y = (x ± √(x^2 +36) )/2
    and sub that into dy/dx to get only x's

    so I will wait for your clarification before I start that messy substitution.

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