Doug C. answered • 04/21/16

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Hi Morgan,

Use implicit differentiation to find y' (a formula for slopes of tangent lines to the given curve).

Something like:

3x

^{2}+ 3y^{2}y' = 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 - 6x

^{2})/(6y^{2}- 9x) --this is with 4.5 returned to 9/2 and complex fraction simplified.