Doug C. answered 04/21/16
Math Tutor with Reputation to make difficult concepts understandable
Use implicit differentiation to find y' (a formula for slopes of tangent lines to the given curve).
3x2 + 3y2y' = 4.5xy' + 4.5y (product rule on right hand side)
Get terms with y' on LHS, other terms on the RHS, factor out the y' and then divide by the binomial after the y'.
y' = (9y - 6x2)/(6y2 - 9x) --this is with 4.5 returned to 9/2 and complex fraction simplified.