using impliciate deferation find y^2+X^3=3XY

Question

This was a homework question and I have a mental block and do not know where to begin.

Answer 1

y^2+x^3 = 3xy

Apply derivative on each side with respect of x.

2yy'+3x^2 = 3(xy'+y)

2yy'+3x^2 = 3xy'+3y

2yy'-3xy' = 3y-3x^2

y'(2y-3x) = (3y-3x^2)

y' = (3y-3x^2)/(2y-3x)