I know i use the product rule but I keep getting the wrong answer

dx/dt | (x=3) = 27/2

Explanation:

x*y = 2 (a)

At x = 3, (3)*y = 2 => y = 2/3

Differentiate (a) wrt t,

x.dy/dt + y.dx/dt = 0 (b)

Put x=3, dy/dt=-3 and y=2/3 in the differential equation (b),

3(-3) + (2/3)*dx/dt = 0

dx/dt = (9*3)/2 = 27/2

it would be 6xy and -16xy.