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I managed to get [tex]dy/dx = 3 / (6y + 8)[/tex] but I have no clue where to go from here.

According to WolfRamAlpha, the answer is [tex]-27/(4(16 + 9x)(4 + 3y))[/tex], but since dy/dx doesn't have any x value in it, I don't see how the derivative of it would.

I've played around with it for a long time, and I just can't get it. Help please?