The slope of the tangent is where the derivative is 0. So you have to use product rule and implicit differentiation to get:

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

Solving for y':
3y^2 y' - 3xy' = 3y - 3x^2
y' [3y^2 - 3x] = 3y - 3x^2
y' = (3y - 3x^2) / (3y^2 - 3x)
y' = (y - x^2) / (y^2 - x)

When y' = 0 gives 0 = y - x^2 => At (x, y) the gradient is m = x^2/y

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