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Verified answer
Y = (x^2)/2 - 3/(x^2)y = 1/2 x^2 - 3x^(-2)
dy/dx = 1/2 (2) x^(2 - 1) - 3(-2) x^(-2 - 1)
= x + 6x^(-3)
= x + 6/(x^3)